The government struck a deal with Brussels last week on three priority separation issues, paving the way for EU leaders meeting on Thursday and Friday to approve the start of trade talks.
Updating parliament on the terms of the financial settlement, rights of European citizens and the Irish border after Brexit, May drew plaudits from all sides of her Conservative party.
"We are going to leave but we are going to do so in a smooth and orderly way" she told MPs, to cheers.
"That's my mission. That is this government's mission. And on Friday we took a big step towards achieving it."
Despite praising her efforts, a number of Conservative MPs raised concerns about the money Britain would pay as it leaves the bloc, estimated at £35 billion to £39 billion (40-45 billion euros, $47-52 billion).
May said the settlement was "fair" and stressed Britain would honour its commitments.
But she added: "This offer is on the table in the context of us agreeing the partnership for the future... If we don't agree that partnership, then this offer is off the table."
Brexit Secretary David Davis prompted alarm in Dublin and Brussels on Sunday by appearing to pull away from guarantees made in the deal over the Irish border.
But May made clear that "it is right that we ensure no new barriers are put in place" between EU member Ireland and the British province of Northern Ireland.
She repeated the EU's mantra that "nothing is agreed until everything is agreed", but said the agreement had created a "new optimism" in the talks.
'Give and take'
Some have viewed the guarantees on the Irish border as a move towards a softer break with Brussels.
The deal holds out the prospect of Britain remaining aligned with some of the rules of the EU's single market and customs union if no new bilateral trade deal is reached.
May said this was a "fall-back option of last resort" and confirmed once again that Britain as a whole would be leaving the EU's single market and the customs union.
Mindful of the ability of hardline eurosceptic Conservatives to disrupt her minority government, the prime minister emphasised there had been "give and take" on both sides.
Speaking after chairing a meeting of her cabinet ministers, many of whom are divided on Britain's future outside the EU, she insisted: "This is not about a hard or a soft Brexit."
She added: "This is good news for people who voted Leave, who were worried we were so bogged down in tortuous negotiations it was never going to happen.
"And it is good news for people who voted Remain, who were worried we were going to crash out without a deal."
Leading Brexit supporter Iain Duncan Smith, a former Conservative party leader, said the agreement was "not ideal" but "simply gets us through the first round".
Uncertainty over deal
However, Labour leader Jeremy Corbyn accused May of having "scraped through" with an agreement that remained unclear, and accused cabinet ministers of contradicting themselves.
Davis said Monday that his suggestion that the Irish border deal was "more a statement of intent than it was a legally enforceable thing" had been "twisted".
Joe McHugh, the Irish government's chief whip, had said it would be "bizarre" to agree a deal and not uphold it.
European Commission spokesman Margaritis Schinas confirmed the agreement was not yet legally enforceable, but said it should be viewed as a "deal between gentlemen".
"It is a clear understanding that it is fully backed and endorsed by the UK government," he said.
The agreement also sets out residency rights and benefits available to more than three million EU citizens living in Britain and another one million of its citizens living in the EU -- as well as their families.
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