This means that as well as the current "take it or leave it" vote in principle on the Brexit deal, the final agreement will need to be enshrined in law and, importantly, be subject to scrutiny and a vote by MPs and peers.
But the proposal triggered an immediate backlash from rebels within May's own party.
Davis's move was seen as an attempted concession to Conservative rebels who may defy the government this week by voting against separate Brexit legislation transferring existing European Union laws to Britain. "We can't have a withdrawal deal bill if there is no withdrawal bill", he admitted in response. There'd be no time!
Fellow Conservative MP Antoinette Sandbach similarly labelled the Government's promise "meaningless" should Brexit talks slip beyond March 2019.
David Davis has caved in to demands for MPs to vote on a separate Bill to implement any Brexit agreement, to head off a major Tory revolt.
"By announcing this bill, we are providing clarity and certainty - both in the negotiations and at home - about the final agreement being put into United Kingdom law". Even if time is on the government's side, there are also so many different parties involved in achieving the final deal that it seems unlikely Parliament could just keep sending Davis back to Brussels until he got is just right. "This agreement will only hold if parliament approves it".
In a statement to the House, the Brexit Secretary appeared to perform a U-turn as he announced that the final Brexit deal will take the form of an act of Parliament.
Chris Leslie, also from the main Labour opposition, called it a "sham offer" that was "totally worthless".
"It's a transparent and fairly desperate attempt at the eleventh hour to save face and avoid losing votes in the House".
"(Mr Davis) has to do much better than this.
The Government has bolstered its commitment for Parliament to have the final say on a Brexit deal - but immediately faced a backlash for not guarding against the United Kingdom leaving the European Union without an agreement.
"He gave no guarantee of a meaningful vote before 29 March 2019 and this doesn't cover the event of there being no deal", he wrote on Twitter.
He said the bill must be amended "to provide for a proper, not a fake, meaningful vote before any exit day".
Earlier, European business leaders warned Theresa May that jobs and investment in the United Kingdom could be lost unless urgent progress is made in the Brexit negotiations with Brussels.
The Cabinet minister added it was down to political will and he was "quite certain the political will is there".