Esther McVey also resigned as work and pensions secretary.
In her letter, she said the deal put forward “does not honour the result of the referendum”.
“Indeed, it does not meet the tests you set from the outset of your premiership,” she added, Euronews reports.
Earlier this morning I informed the Prime Minister I was resigning from her Cabinet pic.twitter.com/ZeBkL5n2xH
— Esther McVey (@EstherMcVey1) November 15, 2018
Earlier in the morning, Shailesh Vara posted his own resignation letter on Twitter.
With much sadness and regret I have submitted my letter of resignation as a Northern Ireland Minister to the Prime Minister. A copy of my letter is attached.
It has been a joy and privilege to serve in the Northern Ireland Office and I will always cherish the fondest memories. pic.twitter.com/SN8j4OwhYD— Shailesh Vara MP (@ShaileshVara) November 15, 2018
Vara, who is not part of the Cabinet which met yesterday to approve the deal on behalf of the government, said in his resignation letter that he could not support the agreement because it obliges the UK to continue to follow EU rules for an undefined period.
“We will be locked in a Customs Arrangement indefinitely, bound by rules determined by the EU over which we have no say. Worse, we will not be free to leave the Customs Arrangement unilaterally if we wish to do so,” he wrote.
The ‘Customs Arrangement’ obliges the UK to adhere to regulations around trade rules in order to avoid putting in place border controls between Northern Ireland, part of the UK, and Ireland, which remains in the EU.
The resignation highlights the challenge May will face getting the deal approved by parliament where hardliners in favour of remaining inside the EU and supporting a Brexit that leaves the UK completely free from Brussels influence have expressed opposition.
Suella Braverman, a junior minister in Britain’s Brexit ministry, also resigned shortly after Raab.
“I now find myself unable to sincerely support the deal agreed yesterday by cabinet,” she said in a letter posted on Twitter.
Braverman said the proposed Northern Ireland backstop is not what the British people voted for, and threatened to break up the UK.
It is with deep regret and after reflection that I have had to tender my resignation today as a Brexit Minister. Thank you for the opportunity. I look forward to working to support Brexit from the Backbenches. This has not been an easy decision. pic.twitter.com/C0kply8aLE
— Suella Braverman MP (@SuellaBraverman) November 15, 2018