But it now needs to be approved by the United Kingdom's Parliament before it can take effect.
He added it was reckless for anyone to maintain there was an alternative to the backstop.
Phillip Schofield and Rochelle Humes brought the Prime Minister on to gain some clarity for the deal she has proposed thus far.
Meanwhile, Mrs May is facing a battle on a second front with Labour threatening to combine with other parties - including the DUP - to force ministers to publish the legal advice given by Attorney General Geoffrey Cox.
"The question now is whether Theresa May can win the "meaningful vote".
Parliamentarians will have their chance to approve or reject the deal in what has been called a "meaningful vote".
He admitted there were aspects of the deal he found "uncomfortable", but said his message to MPs was that they "should not make the ideal the enemy of the good".
However, Starmer said seeking a confidence vote against May would be inevitable if she loses the Brexit vote.
But the government has insisted it would instead publish a reasoned statement, citing a need for Cabinet confidentiality.
He told The Associated Press on the sidelines of the global climate conference in Katowice, Poland, that "when you take all these red lines into account it's simply impossible to come up with something different than we have now, the deal on the table".
And Mr Gyimah, who until Friday was a science minister, said the government had a duty to "level with the public".
May has said Britain would look to build its own system.
Boris Johnson, who resigned from government over the PM's Brexit vision, described the arrangement in his weekly Daily Telegraph column as "a great steel trap that is about to clamp its jaws around our hind limbs and prevent our escape".
British Prime Minister Theresa May said Saturday she was determined to win lawmakers' backing for her Brexit deal, after a minister who quit her government said her divorce agreement would leave Britain outnumbered and outmaneuvered in future negotiations with the European Union.
Gyimah, who voted to remain in the European Union, said the deal was "not in the British national interest" and that voting for it would set Britain "up for failure".
He said he had supported Mrs May after her "awful" party conference speech and "appalling" election campaign past year but now "she needs to help herself a bit" by changing course. "We have got to recognize that if we don't vote for this, the alternatives are no deal or no Brexit".
The two-part agreement includes the legally binding terms of the UK's departure and an ambitious but vague declaration about future relations between the two sides.