Mr Johnson confirmed on Wednesday that he will not be backing the deal when MPs vote on the Stormont brake in the Commons later on Wednesday, with Ms Truss set to follow suit.
In a statement, Mr Johnson said: “The proposed arrangements would mean either that Northern Ireland remained captured by the EU legal order – and was increasingly divergent from the rest of the UK – or they would mean that the whole of the UK was unable properly to diverge and take advantage of Brexit.
“That is not acceptable. I will be voting against the proposed arrangements today.
“Instead, the best course of action is to proceed with the Northern Ireland Protocol Bill, and make sure that we take back control.”
A source close to Ms Truss said that she plans to vote against it too.
Ms Truss is understood to believe the Prime Minister’s Windsor pact does not “satisfactorily resolve the issues thrown up by” the Northern Ireland Protocol and “almost fatally impinges” on the UK’s ability to diverge from EU rules and regulations.
With Labour backing the Windsor Framework agreement signed last month, the Government should win the Commons division comfortably, despite criticism from some hardline Tory Brexiteers.
The DUP has already said its eight MPs will vote against the regulation to implement the Stormont brake as it continues to seek changes to the overall framework.
The confirmation by Mr Johnson of his opposition to the UK-EU deal comes ahead of his appearance before the Privileges Committee, where he will be grilled by MPs investigating claims that he knowingly misled Parliament over the partygate affair.
The former prime minister, who agreed the original Northern Ireland Protocol with Brussels as a way to avoid a hard border on the island of Ireland, had earlier this month indicated that he would find it “very difficult” to support the Windsor agreement.
It remains to be seen how large a rebellion Mr Sunak will face, when the secondary legislation on the Stormont brake comes before MPs.
On Tuesday, the European Research Group (ERG) said the brake, which is intended to provide a veto on the imposition of new EU regulations in Northern Ireland, is “practically useless” following an analysis of the framework by its “star chamber” of lawyers.
Eurosceptic members have not yet decided how to vote, with the group set to meet later on Wednesday.
Foreign Secretary James Cleverly is due to meet the EU’s Maros Sefcovic in London on Friday to formally adopt the Windsor pact at a meeting of the joint committee on the Withdrawal Agreement.
While the DUP is not in a position to block it, their opposition suggests that an early return to powersharing at Stormont is highly unlikely.
The Executive and Assembly have been suspended since the DUP walked out last year in protest at the way the protocol was operating, saying it weakened Northern Ireland’s position in the UK.
Downing Street has indicated that there could be further votes in the weeks ahead on the statutory instruments needed to implement other elements of the framework.
However, there is frustration among some MPs that Mr Sunak is resisting calls for an overall vote on the whole framework document.
Conservative backbencher Peter Bone said he is “pretty miffed” about the Government’s approach to a vote as he signalled that he could join Mr Johnson in voting against this part of the deal.
“I’m really pretty miffed that the Government is avoiding scrutiny on this, and on the brake itself, it seems to fail all the tests,” Mr Bone, who was deputy leader of the House for three months last year, told Sky News.
“If that is the case, I’m going to listen to the debate. I’m going to go meetings this morning, but, if I had to vote at this moment in time, I should vote against.”