Mr Cameron said: "Of course, Ian Paisley was a controversial figure for large parts of his career. Yet the contribution he made in his later years to political stability in Northern Ireland was huge.
"In particular, his decision to take his party into government with Sinn Fein in 2007 required great courage and leadership, for which everyone in these islands should be grateful."
Mr Cameron's predecessors, Tony Blair and John Major, and Northern Ireland First Minister Peter Robinson lauded an implacable opponent of compromise who became a peacemaker.
Mr Blair, who presided over the restoration of devolved government in Northern Ireland through the Good Friday Agreement in 1998, said: "Ian was a man of deep convictions. The convictions never changed. But his appreciation of the possibilities of peace, gradually and with much soul searching, did. He began as the militant. He ended as the peacemaker."
Sir John Major voiced his "great admiration and respect" for the former DUP leader, who was a fierce opponent of the Downing Street Declaration which the former prime minister signed in the early stages of the peace process in 1993.
He said: "Ian Paisley was a man of public passion and huge personal charm, who cared deeply for the community he served.
"From a position where he was suspicious of every movement towards peace, he came to embrace it, and served as the first First Minister of Northern Ireland. It was a remarkable journey by a remarkable man, for whom I had great admiration and respect."
Mr Robinson said the former leader inspired the DUP.
He told BBC Radio 4's World at One: "He was a colossus in Unionism and made such a massive contribution, particularly to the process in which we are presently involved."
Mr Cameron said he saw Dr Paisley most in the House of Commons, where his great oratory stood out.
"He had a deserved reputation as one of the most hard working and effective MPs.
"Ian Paisley will be remembered by many as the 'big man' of Northern Ireland politics. He will be greatly missed."
His wife, Baroness Eileen Paisley, said: "My beloved husband, Ian, entered his eternal rest this morning.
"Although ours is the grand hope of reunion, naturally as a family we are heartbroken.
"We loved him and he adored us, and our earthly lives are forever changed."
Former IRA commander Martin McGuinness expressed regret and sadness.
"Over a number of decades we were political opponents and held very different views on many, many issues, but the one thing we were absolutely united on was the principle that our people were better able to govern themselves than any British government.
"I want to pay tribute to and comment on the work he did in the latter days of his political life in building agreement and leading unionism into a new accommodation with republicans and nationalists."
Mr Blair said over time he got to know Dr Paisley well.
"He could be an uncompromising even intransigent opponent. But he was also someone who loved Northern Ireland and its people. He led them but he also followed them. When they said to him peace was thinkable, he made it possible.
"His religious beliefs were profound and genuine. He talked to me often about the need for forgiveness and I am sure part of what made him finally take the road to peace was his capacity, driven by his Christian belief, to contemplate and then work for reconciliation.
"I don't suppose 40 years ago he would ever have thought that politically his life then would end as it does now. But I know he and Eileen would be very proud of his huge contribution to a peaceful future for Northern Ireland."
Mr Robinson added: "He was more than a significant figure. Ian was a founder and inspiration behind the existence of the party. He led it through difficult times where the Unionist community in Northern Ireland was under attack from terrorism and felt that their constitutional position was imperilled, right through from those dark days to the relative peace and security that we have at the present time.
"He was instrumentally involved and a key figure in terms of entering into the agreements that made it all possible."
Northern Ireland Secretary Theresa Villiers said for more than five decades he was a dominant figure in Northern Ireland politics through his booming oratory and enormous personality.
"He was unswerving in his commitment to Northern Ireland's position within the United Kingdom. Yet he was, by his own admission, first and foremost a preacher.
"It is undoubtedly the case that he was often controversial in pursuing his goals. For now, however, it is right that we focus on the contribution he made to the Northern Ireland peace process, particularly in taking his party into government in 2007.
"From his election in 1970 through his elevation to the Lords in 2010, Ian Paisley was a formidable parliamentarian. He was also a tireless and highly effective MP on behalf of all his constituents. Ian Paisley had a deep reverence for Parliament and its traditions. Parliament has lost one of it great characters."
Former prime minister Gordon Brown said few have had as massive an influence on the recent politics of the United Kingdom as Ian Paisley.
"His support for the peace process was vital in moving it forward. He will be remembered as a powerful preacher, a moral campaigner and a popular orator who combined humour and passion."
Irish premier Enda Kenny said Dr Paisley was by any measure a major figure in the history of Ireland and Britain.
"I had the pleasure of meeting and talking to him in recent years, and I know that he treasured the peace and friendship that he had lived to see, and helped to build, between our traditions.
"His devotion to his faith and to the unionist people of Northern Ireland was deep and unshakeable."
Sinn Fein president Gerry Adams, a TD in the Irish parliament, said he was deeply shocked and saddened at Dr Paisley's death.
"There will be plenty of time for political analysis but at this point I wish to extend my deepest sympathies to Ian's wife Eileen and to the Paisley family at this very sad time," he added.
Former Irish taoiseach Bertie Ahern said: "Ian was a big man. He had a big heart.
"In my younger days I found him a very difficult character but we ended up very good friends. He was a valuable character in the peace process."
Mr Ahern said Dr Paisley's latter years saw him pay a big price politically and personally, in friendships and in his vocation to the Free Presbyterian Church, after some of his associates of the previous 40 or 50 years deserted him.
"I grew to admire him. The more I got to know him, the more I grew to like him," he told RTE Radio.
Former Northern Ireland secretary Peter Hain said: "Ian Paisley was the big man of Northern Ireland politics. The historic 2007 peace settlement bringing bitter lifetime enemies to govern jointly could never have happened without him.
"I worked very closely with him and came to like and respect him, his wife Eileen, his MP son Ian and his wider close-knit family to whom I extend my sympathies."
Former nationalist SDLP leader Mark Durkan told BBC Radio 4's World at One: "He went from vicious rhetoric during the '70s to playing a virtuous role.
"The fact is that even though he absolutely opposed the Good Friday Agreement and all the agreements attempted before that, he ended up helping to seal the settled process that we now have, accepting power-sharing, North-South institutions and all the rest of it, and working in a good spirit."
Mr Durkan, who served as Stormont deputy first minister from 2001 to 2002, said Mr Paisley would be remembered as "someone who opposed initiative after initiative, who brought down various Unionist leaders and contributed to many lost years and lost opportunities, only in the end to accept things that he had always opposed, but actually to work within them with some grace".
Archbishop of Canterbury Justin Welby expressed his condolences to the family.
"He was a passionate advocate for his community, a parliamentarian who made his presence felt in our national life and a man of deep faith.
"History will remember him for many things but above all for having the courage, when he judged the moment to be right, of taking the difficult but vital steps towards reconciliation."
Labour leader Ed Miliband said he was a towering figure.
"His decision to take the DUP into a power-sharing partnership with Sinn Fein was the ultimate act of political courage and reconciliation.
"His willingness to work positively with Martin McGuinness was a key element in ensuring continued peace and stability in Northern Ireland."
Scotland's First Minister, Alex Salmond, said: "Ian Paisley was a major figure in the politics of these islands who I first got to know at Westminster as a warm, personable fellow MP, despite the obvious differences in our political outlook.
"He and I became First Ministers in the same month and it was a matter of considerable pride that my first speech outside Scotland in that role was at the Assembly in Belfast, where I was warmly welcomed by Dr Paisley, by the Deputy First Minister and other ministers in the power-sharing Executive.
"His long political journey to become Northern Ireland's First Minister, ultimately sitting down with his long-time opponents and playing a critical role in promoting reconciliation across communities, is well-documented and will leave a precious and enduring legacy.
"His passing will be mourned across Northern Ireland, as it will be in Scotland and further afield. I send my condolences to his wife Eileen and to his wider family and friends."
President of Ireland Michael D Higgins described Mr Paisley as a man of deep convictions.
"Irrespective of one's political perspective, Dr Paisley was undoubtedly a man of immense influence on the contemporary history of this island," the president said.
"His early career was characterised by an uncompromising position of a constitutional kind. However, his embracing of the change necessary to achieve a discourse that might lead to peace was of immense significance, as was his commitment to building relationships in support of that peace."
European Commission President Jose Manuel Barroso said he was saddened.
"Throughout his career as a domestic and European parliamentarian, as well as in his ministry, he held strong views and expressed them with passion.
"In 2007 as First Minister of Northern Ireland he led a historic power-sharing partnership which set the province on a historical path to a lasting peace.
"When I visited Northern Ireland in May that year, I saw for myself Ian's personal drive, energy and commitment to peace and stability.
"I am pleased that the European Commission has been able to actively contribute to supporting Northern Ireland in this process through the work of the PEACE programme and the Task Force for Northern Ireland."
Mr Barroso added: "I would like to convey my condolences to Ian's family at this saddest of times."
He was one of Northern Ireland's best-known political figures, but it will be in the Bible-belt town of Ballymena, in Co Antrim where Ian Paisley's death will be felt the most.
News of his death spread quickly throughout the close-knit mainly Protestant market town about 25 miles north of Belfast where the firebrand preacher was consistently returned as an MP for almost 40 years.
Doreen Mairs, 71, a semi-retired supermarket worker from Ballymena, said his death had taken her by surprise.
"I was shocked to hear about it, although I did know he had been ill," she said. "I am not into politics but I know he certainly had his views.
"I have to say I was surprised when he went into government at Stormont in the way it is. But, I suppose he had his reasons."
Although he was a divisive force on constitutional issues even Mr Paisley's critics admit that he fought diligently for local constituents.
Billy Workman, 62, a retired factory worker from the Harryville area of Ballymena, said: "It is a very sad day. I saw Ian Paisley as one of Northern Ireland's great statesmen and in my view he will be remembered as being a great democrat. He was a very honourable man who stood up for what was right.
"I know he had his critics but he should be remembered for all the work that he has done - especially for this town."
Ian Paisley was not born in Ballymena but is widely regarded as one of its most famous sons. In 2004 Ballymena Borough Council conferred on him its highest honour, making him a freeman of the town.
Retired accountant William Agnew. 62, described the former DUP leader and preacher as an astute politician who would be best remembered for his hard-line stance against the Sunningdale Agreement during the 1970s.
He said: "He was a bit of a trouble maker in the early days and I think he'll be best remembered for his part in the Ulster Workers' Strike.
"His death was not unexpected because we knew he had been ill."
But not everyone was mourning him.
One woman, who declined to be named, describing herself as a Catholic from Harryville, claimed Mr Paisley had helped prolong the Troubles.
She said: "I think this country could have been sorted out a lot sooner if Ian Paisley had not been involved,
"And I believe he only became First Minister because he was in the last throes of his political life."