The 39-year-old passed away over the weekend. He is survived by his wife Laura and their four young children.
Today, colleagues at Stormont and beyond set aside political differences to pay their respects to the South Belfast representative.
Sir Jeffrey said Mr Stalford “believed in stretching himself to build a genuinely shared future”.
Passing on his sympathies to Mr Stalford’s family, he recalled a “precious” last conversation with his friend on Friday night.
In an interview this afternoon, Sir Jeffrey told how he and colleagues were “absolutely devastated” to learn of his death this morning.
He added: "Christopher was first and foremost a loving husband, a father and a son and anytime you talked to Christopher he was always wanting to talk about his family.
"I had a conversation with him on Friday and we were talking about political matters and the forthcoming elections. But, of course, Christopher talked about school, about children moving to the big school.
"He just lived for his family, but he also lived for his politics and Christopher loved representing his constituency of South Belfast, he wanted to work for everyone."
Sir Jeffrey said the party is also also grateful for the many messages from other political parties.
"Christopher had the capacity to reach out across the political divide and he was someone who wasn't afraid to do the heavy lifting and to push the boundaries and to try and make Northern Ireland a better place for all of us," he added.
Mr Stalford and his wife, Laura, a former dental nurse, have four children.
Mr Stalford was elected as a Belfast councillor in 2005 to represent the Laganbank area and then, from 2014, represented the Balmoral area.
He was elected the High Sheriff of Belfast in 2010 and Deputy Lord Mayor of Belfast in 2013.
In 2016, Mr Stalford was elected to represent Belfast South in the Northern Ireland Assembly, and from January 2020 he served as the principal deputy speaker of the Assembly.
Sir Jeffrey added: "I've no doubt that one day Christopher would have been the Speaker of the Northern Ireland Assembly, something that would have made him immensely proud, given the very humble background that he came from.
"Christopher was very articulate, he made some fine speeches in the Assembly.
"He also had a great sense of humour. Even in dark moments, Christopher had the capacity to just lift the mood, say something that would bring a little bit of light into a very difficult situation.
"He was passionate about working for a better future.
"Our political world today is, I'm afraid, a sadder place without Christopher."
Mr Stalford has been involved with the DUP since he graduated from Queen's University in Belfast.
He went to work in former DUP member Jim Allister's European office three days a week, and in Peter Weir's Bangor office.
He then moved to the DUP press office for six years, and went on to the policy unit.
In 2005, he was elected to Belfast City Council aged 22, the youngest person on the council.
He ran for the Northern Ireland Assembly in 2007 but did not get elected, and was re-elected to the council in 2011 and 2014.
Mr Stalford then got elected to the Assembly and had been working as an MLA in South Belfast for the last six years.
I have been really struggling to process the news of Christopher’s death, but my first thoughts and my prayers are with Laura and his beloved and adored children. This is how I will remember him, happy and confident after the 2016 election. Matthew 5v4. pic.twitter.com/nVbz02wor5— Arlene Foster #ProudofNI. (@ArleneFosterUK) February 20, 2022
Former DUP leader Arlene Foster said she was “struggling to process” Mr Stalford’s death but will remember him as “happy and confident” following his 2016 Assembly election success.
DUP chairman Lord Morrow said he had known Mr Stalford since his childhood and that his family were “faithful members” of the party from its foundation.
“From his earliest days, Christopher was immersed in the politics of Northern Ireland,” he said.
“He was a committed unionist and was always destined to be an elected representative because he had a heart for the people, public service and making Northern Ireland better.
“We thank those across the political spectrum for their condolences and thoughtfulness. We ask that Christopher’s family are given privacy and space to grieve.”
Secretary of State Brandon Lewis and Taoiseach Micheal Martin were also among those to send messages of condolence today.
"As MLA and principal deputy speaker, Christopher was passionate about crucial issues that affected people across NI and was dedicated to building a better Northern Ireland for everyone," Mr Lewis said.
UUP leader Doug Beattie added that no matter their differing political views, they never “traded an angry word”.
Sinn Fein vice-president Michelle O’Neill expressed her sincere sadness following Mr Stalford’s passing.
"His friends and colleagues throughout the world of politics will miss his political contribution, and his constituents his local efforts and leadership across south Belfast," she added.
SDLP leader Colum Eastwood, who postponed his party’s Spring conference on Sunday as a mark of respect, expressed his shock and said no matter how heated an Assembly debate could become, Mr Stalford “would always have a wry smile and a laugh” when it was over.
The TUV’s Jim Allister said he retained “friendship and respect” for the MLA, while Alliance Party leader Naomi Long said they shared a “warm personal friendship”.
Mr Stalford’s funeral details will be made public in due course.