The new Brexit Secretary has been confirmed as Dominic Raab.
The 44-year-old's appointment comes less than 12 hours after former secretary of state for exiting the European Union, David Davis, quit over the Government's Brexit plan which he said he could not back as he does not believe in it and does not think it will deliver the "proper Brexit" people voted for in the EU referendum.
ITV News Political Correspondent Carl Dinnen reports that although former housing minister Mr Raab is a Brexiteer, many others are "unhappy" with the appointment.
Despite signing up to the strategy agreed at Chequers on Friday, Mr Davis quit late on Sunday night.
Faced with accusations that his resignation would weaken the Government's negotiating position over Brexit, Mr Davis said his actions would instead "strengthen" it.
The resignation of her former Brexit secretary is thought to have left Theresa May facing a potential leadership crisis, but Mr Davis said he fully supports her as she is a "good Prime Minister".
On Monday morning, Mr Davis said he made it "very clear" during Friday's Cabinet meeting that he was the "odd one out" and did not agree with the Prime Minister's plan because there was a "risk of it delivering a poor outcome".
Speaking to ITV News Political Editor Robert Peston, Mr Davis said his resignation was one of "principle", since he did not agree with the Government's Brexit strategy on a number of points.
He argued that the proposals would deliver a "soft Brexit", and spoke of his reservations of the UK collecting tariffs for the EU, and also the influence the European Court of Justice (ECJ) would retain in the country once the UK leaves the EU.
The 69-year-old continued that the plan also "volunteers" too much information to the EU, weakening the UK's negotiating position and also making it likely that the EU would take what was offered to them and then ask for more.
Mr Davis continued that while he did not agree with the Government's Brexit plan "it is central to my old brief, it would have been me who would have had to present it to Parliament, it would have been me who would have had to carry it out, me that had to make it work in the European Union, and frankly if I don't believe in it, I'm not the best person to do it".
Mr Raab is a staunch Brexiteer and Peston writes that Mr Davis sees him as a protegee.
The departure comes as the Prime Minister sets out to win over Tory Brexiteers after a backlash against her plans for leaving the European Union.
Mr Davis' junior ministerial colleague Steve Baker has also quit his role.
In his resignation letter, Mr Davis told Mrs May he believed "the current trend of policy and tactics" is making it look "less and less likely' that the UK will leave the customs union and single market, adding: "The general direction of policy will leave us in at best a weak negotiating position, and possibly an inescapable one."
The responsibility for leading the negotiations should now go to an "enthusiastic believer in your approach, and not merely a reluctant conscript", he said.
In response, the Prime Minister told Mr Davis: "I do not agree with your characterisation of the policy we agreed at Cabinet on Friday."
She said: "I am sorry that you have chosen to leave the Government when we have already made so much progress towards delivering a smooth and successful Brexit and when we are only eight months from the date set in law when the United Kingdom will leave the European Union."
ITV News Political Editor Robert Peston says Mr Davis' resignation represents the greatest test to Theresa May's authority since she became Prime Minister and that "there may well be a leadership contest before the summer".
Mr Davis also told Peston that he did not think his resignation would weaken the Tory Party or leave Mrs May facing a leadership crisis, adding that he is "a supporter of the Prime Minister, I think she's a good Prime Minister, I just don't agree with her on this fundamental policy".
Earlier Mr Davis told BBC Radio 4's Today programme that should Mrs May resign, or be forced out as Prime Minister, he "would not throw my hat into the ring" to replace her.
Mr Davis' resignation was warmly welcomed by hardline Eurosceptics in the Tory ranks who were already expressing reservations about Mrs May's leadership after her Cabinet agreed a plan which would keep the UK closely tied to Brussels.
Arch-Brexiteer Jacob Rees-Mogg, leader of the powerful European Research Group faction within the Tory ranks, said Mr Davis' resignation should force Mrs May to reconsider her approach to Brexit.
Meanwhile Labour leader Jeremy Corbyn said Mrs May "has no authority left and is incapable of delivering Brexit".
On Monday, Mrs May is expected to tell MPs that the strategy agreed on at Chequers is the “right Brexit” for Britain.
But resistance to the plan from hardline Eurosceptics grew over the weekend.
Mr Rees-Mogg hit out at the “defeatism” in the Government’s plans, warning that he would vote against them – and suggested other Eurosceptics may do the same.
In the Commons, Mrs May will acknowledge that there have been “robust views” around the Cabinet table and a “spirited national debate” since the 2016 referendum decision to leave the EU.
She will say: “Over that time, I have listened to every possible idea and every possible version of Brexit. This is the right Brexit.”
She will tell MPs it was “the Brexit that is in our national interest” and “will deliver on the democratic decision of the British people”.
The Prime Minister will insist the plan, which would see the UK share a “common rulebook” for goods as part of a proposal to create a UK-EU free trade area, still meets her Brexit red lines.
But Mr Davis’ decision could now act as a spur to other Brexiteers to take action against Mrs May.