- Video report by ITV News Political Editor Robert Peston
The prime minister has secured "legally-binding" changes to the Brexit Withdrawal Agreement.
In a joint press conference in Strasbourg Theresa May and European Commission President Jean-Claude Juncker confirmed the breakthrough in the Brexit deadlock.
Mrs May urged MPs to "come together", hours ahead of Tuesday's Meaningful Vote.
She told journalists a "joint instrument with comparable legal weight to the Withdrawal Agreement will guarantee that the EU cannot act with the intent of applying the backstop indefinitely".
She added that "if the backstop comes into use and discussions on our future relationship breakdown...then it is the position of the UK that there would be nothing to prevent the UK instigating measures that would disapply the backstop".
In a tweet Mr Juncker said "the agreement provides meaningful clarifications and legal guarantees to the Withdrawal Agreement".
He added: "The choice is clear: it is this deal, or Brexit may not happen at all."
Ahead of the press conference the the prime minister's de-facto deputy, Mr Lidington, told MPs in the Commons: "Tonight we will be laying two new documents in the House; a joint legally-biding instrument on the Withdrawal Agreement and protocol on Northern Ireland and a joint statement to supplement the political declaration.
"The first provides confirmation that the EU cannot try to trap the UK in the backstop indefinitely and that doing so would be an explicit breach of the legally-binding commitments that both sides have agreed."
And he said the "joint instrument" reflects the commitment to "replace the backstop with alternative arrangements by December 2020".
Mr Lidington added the Attorney General would be publishing advice ahead of Tuesday's debate, but needed time to consider the new changes.
"The Attorney General will publish his legal opinion," he said. "That will be available in good time before the debate.
"I think the house would expect the Attorney General to consider very carefully rather than rush an opinion out to meet the deadline for this statement this evening."
The last-ditch bid to make progress in talks came amid predictions the prime minister was headed for a second humiliating defeat on her Withdrawal Agreement and it remains to be seen if the concessions will be enough to see it pass through Parliament.
Shadow Brexit secretary Sir Keir Starmer said the change "adds nothing" from the letter Mrs May returned from negotiations with on January 14.
He said: "If all that's happening is to turn this letter into an interpretative tool for legal purposes, I remind the House what the prime minister said on January 14 about this letter.
"She said she had been advised this letter would have legal force in international law.
"To stand here today and say this is a significant change when she's repeating what she said on January 14 is not going to take anyone here far."
Time is running out for any new assurances or clarifications to the deal which was resoundingly rejected by a 230-vote majority by MPs in January.
- ITV News Political Editor Robert Peston explains what to expect from tomorrow's Meaningful Vote
Brexit minister Robin Walker confirmed a second meaningful vote on Theresa May's deal will take place on Tuesday.
Mr Walker was jeered by Labour MPs as he explained he had been sent because negotiations were "at a critical stage".
Mr Corbyn used the question to say the Government is in "chaos" over Brexit.
If her deal is rejected again on Tuesday, the Labour leader said the PM should "shift her red lines and show not just that she is willing to meet with members of this House, but that she is willing to compromise with them too".