Theresa May's top Brexit negotiator Olly Robbins will quit his this summer.
The civil servant who led the outgoing PM's Brexit talks will step down shortly after the new prime minister takes up his post at the end of July.
It is understood he will take a job in the private sector.
It comes as the frontrunner to replace Mrs May Boris Johnson threatened an increasingly aggressive break with Mrs May's position - which has included refusing to rule out suspending Parliament to stop MPs blocking Britain crashing out without a deal..
As the campaign to replace her continues, Mrs May will head to Brussels for a European Council summit where EU heads of state will continue discussions on who should be nominated for the EU's top jobs.
Mrs May will step down following her final PMQs on Wednesday July 24 and Mr Robbins is expected to follow shortly afterwards, although he has committed to a brief handover before he moves on, with reports he may take up a job in the City.
Mr Robbins's departure is the latest in a wave of top civil servants dealing with Brexit who have announced they will resign rather than take on the challenge of delivering Brexit within 100 days under the new leader.
Tom Shinner, director of policy and delivery coordination at the Department for Exiting the EU, and Karen Wheeler, director general of Her Majesty's Revenue & Customs Brexit border delivery group, have both announced they will quit.
Mr Hunt was asked about Mr Robbins at a hustings in Manchester and said it was "a good moment to change our approach" to cheers from Tory members.
"I didn't agree with the approach that we took in a number of areas of the Brexit negotiations," he said.
"I was a loyal Cabinet minister - I think it's very important the Prime Minister has a loyal foreign secretary - but I wasn't a believer in the backstop and I didn't believe it would get through Parliament, so I think this is a good moment to change our approach.
"I'm not going to say something about a civil servant who I know works incredibly hard, even though there are issues I disagree with him on.
"But I do think now is a moment that we have to get this right, deliver a different deal and one that can actually get through Parliament."
Mr Hunt is reported to have signed up former Canadian prime minister Stephen Harper to lead his negotiating team, alongside Crawford Falconer and Rona Ambrose, with the aim of securing a Canadian-style free trade deal, while Mr Johnson is said to have recruited Sir Edward Lister.
