He said this should be enough to persuade MPs to vote for the agreement on Tuesday, just 17 days before Britain is scheduled to leave the EU.
"Tomorrow there will be a fundamental choice -- to vote for the improved deal or to plunge this country into a political crisis," he said.
Lidington said two new documents would be put to MPs.
He said London and Brussels had agreed a "joint legally binding instrument" on the withdrawal text that governs Britain's exit terms, and which includes a controversial "backstop" plan to keep open the border with Ireland.
This document "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", he said.
The backstop would keep Britain in a customs union with the EU if and until another way -- such as a new trade deal -- could be found to avoid checks on the Irish border.
If the EU did breach its commitments to try to find an alternative to the backstop, Lidington said Britain could use this legal document "as the basis for a formal dispute through independent arbitration", and ultimately get the backstop suspended.
The document also emphasises that both Britain and the EU want to find an alternative to the backstop by December 2020.
Finally, it would put assurances from European Commission chief Jean-Claude Juncker and European Council president Donald Tusk over the temporary nature of the backstop "onto a legally binding footing", Lidington said.
A second document has also been agreed, supplementing the political declaration which sets out hopes for a UK-EU trade deal, to outline commitments from both sides on moving swiftly to this new relationship.