Arlene Foster has urged Prime Minister-in-waiting Theresa May to plan the UK's exit from the European Union without delay.
The First Minister said she welcomed the news that Mrs May had promised a Brexit in keeping with the referendum result.
"I wish Theresa May every success as she becomes Prime Minister of the United Kingdom and assure her that we stand ready to work with her in the best interests of both Northern Ireland in particular and the United Kingdom as a whole," she said.
"It is important that she can commence work on planning the UK exit and the new arrangements to be negotiated."
Mrs May was announced as the new leader of the Conservative Party yesterday afternoon after her only rival Andrea Leadsom (below) made a surprise decision to pull out of the contest.
She is expected to officially take over at 10 Downing Street tomorrow evening.
Mrs Foster said she was looking forward to "early discussions with our new Prime Minister".
In the DUP leader's statement Mrs May was also praised as having "a positive history of working with the Northern Ireland administrations" on justice issues, such as the National Crime Agency becoming fully operational here.
But Sinn Fein MLA Alex Maskey said he didn't believe Mrs May had a "terribly encouraging history".
"One of the first things she did when she entered the British Government was to remove legislation which was to enable governments to tackle inequalities," he said.
"She wanted to remove the Human Rights Act and she's on record as saying that and she's been part of a Government which has had the austerity programme at its heart for many years.
"Not a terribly encouraging history, but let's see what she's going to do now she's the British Prime Minister."
Northern Ireland Secretary Theresa Villiers said she would love to stay on in the role. She had backed Ms Leadsom, but has now promised her full support to Mrs May.
"I think Theresa May will do a great job, she has my full support and I think now is the start of a process of making a success of the Brexit decision," she said.
Ulster Unionist leader Mike Nesbitt welcomed the early resolution of the leadership contest.
"The UK needs certainty and this is the first small step on the road so that we are not facing a summer of disquiet. We need strong, coherent Government with an effective Opposition," he said.
After a dramatic day at Westminster yesterday, Mrs May promised to give UK people "more control over their lives".
She will become the UK's second female PM after Mr Cameron answers MPs' questions in the Commons for the last time today and then goes to Buckingham Palace to offer his resignation to the Queen.
Labour has already called for a general election, saying it is "crucial" that the UK has a "democratically-elected Prime Minister" at a time of economic and political instability following the vote to leave the EU. Mrs May declared she was "honoured and humbled" to lead the Conservative Party but insisted there would be no poll until 2020. She repeated her message that "Brexit means Brexit", despite being a Remain supporter during the campaign.
At a speech in Birmingham she signalled that she would offer "a different kind of Conservatism" that will "get tough on irresponsible behaviour in big business" and give ordinary workers a greater share in economic growth.
Mr Cameron said he was "delighted" that the 59-year-old Home Secretary will replace him in Downing Street.
Speaking outside Number 10, he said: "She is strong, she is competent, she is more than able to provide the leadership that our country is going to need in the years ahead and she will have my full support."
Northern Ireland right now is in the same position as Larry the Downing Street cat. We've just been saddled with a new owner too, as David Cameron packs his belongings and newly-elected Tory leader Theresa May gets set to move in to Number 10.