Health Secretary Jeremy Hunt was named the new United Kingdom foreign secretary on Monday, according to a tweet from 10 Downing Street.
"The Queen has been pleased to approve the appointment of".
Matt Hancock, previously the Culture Secretary, has been named as the new Health Secretary.
With Britain due to leave the 28-nation bloc on March 29, 2019, European Union officials have warned Britain repeatedly that time is running out to seal a deal spelling out the terms of the divorce and a post-split relationship.
Inside, the paper sets out the possible scenarios: a fightback from May, a Conservative leadership challenge from Boris Johnson or a general election which could see Labour take power.
The departure of the two Cabinet "big beasts" came just two days after Prime Minister Theresa May secured senior ministers' agreement at Chequers for a Brexit plan about which both men had expressed reservations.
He has always supported a so-called "hard Brexit", which supports relinquishing access to the bloc's single market in exchange for full border control.
"My concern is about the policy rather than the individual", he said. Kat Malthouse, a work and pensions minister, replaced Dominic Raab as housing minister and Chris Heaton-Harris became a junior minister at the Brexit department, replacing Steve Baker.
"It seems to me we're giving too much away, too easily, and that's a risky strategy at this time", Davis said in a BBC radio interview Monday morning. But leading pro-Brexit lawmaker Jacob Rees-Mogg said he didn't think she would face a leadership challenge.
Ms Allan offered her support but warned the European Union may try to dilute her proposal, which would lead some MPs to see no-deal as the best solution.
But she said: "We do not agree about the best way of delivering our shared commitment to honour the result of the referendum".
If she chose to fight, she would need the support of more than 50% of Conservative MPs - now 159 - in the confidence vote to stay in office.
"This is the Brexit that is in our national interest".
But in parliament, her words suggested she had made a decision to face down the dissenters rather than change her plans.