The Prime Minister will use her speech in the Commons on Monday to say she "fully hopes and expects" EU27 leaders to allow talks to progress on to trade.
Cautioning that "nothing is agreed until everything is agreed", she will use Friday's agreement to boost the Government's Brexit momentum.
Mrs May is expected to say: "I know that some doubted we would reach this stage.
"I have always been clear that this was never going to be an easy process. It has required give and take for the UK and the EU to move forwards together. And that is what we have done.
"Of course, nothing is agreed until everything is agreed.
"But there is, I believe, a new sense of optimism now in the talks and I fully hope and expect that we will confirm the arrangements I have set out today in the European Council later this week."
She (Munich: SOQ.MU - news) will also tell MPs that moving on to stage two talks will mean the UK can "build the bold new economic and security relationships that can underpin the new deep and special partnership we all want to see".
While Brexiteer Cabinet ministers have all backed Mrs May's deal , and a widespread backbench backlash never materialised, the speech comes in a tricky week for the Government.
Wellingborough MP Peter Bone told Sky News he was "unhappy" with "bits" of the deal , which will see the UK pay a "divorce bill" estimated at between £35bn and £39bn.
And Brexit Secretary David Davis faced a backlash for calling the agreement a "statement of intent".
Irish government chief whip Joe McHugh said Dublin viewed the promise of no hard border as binding.
"My question to anybody within the British Government would be, why would there be an agreement, a set of principled agreements, in order to get to phase two, if they weren't going to be held up? That just sounds bizarre to me."
Remain-backing rebels are also gearing up for a fight on an amendment to give Parliament a "meaningful vote" on the full final deal.
Drafted by former Tory attorney general Dominic Grieve, the proposal would make sure MPs got the final say on an exit package.
Despite the threat, the Government has not lost a single vote on amendments to its EU Withdrawal Bill.
Some MPs have withdrawn their proposals after reassurance their issues will be incorporated in other ways or looked at further.