In a statement to parliament following the preliminary deal reached on Friday with the EU over Britain's divorce bill, citizens' rights and the Irish border, May will say both sides compromised to defy the doubters.
"Of course, nothing is agreed until everything is agreed," she is expected to tell MPs.
"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.
Under the proposed agreement, Britain will pay a financial settlement of between 35-39 billion pound (40-45 billion euros, USD 47-52 billion) for leaving the bloc in March 2019.
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It allows EU citizens living in Britain and its citizens living in the EU -- as well as their families -- to claim permanent residency status, alongside the right to work, study and access healthcare, pension and social security entitlements.
Meanwhile, Britain has vowed to find a way to avoid a hard border between Ireland and Northern Ireland, with the possibility of "full alignment" with the EU single market and customs union rules that are crucial to a 1998 peace accord.
But May will tell lawmakers: "This is not about a hard or a soft Brexit.
"The arrangements we have agreed to reach the second phase of the talks are entirely consistent with the principles and objectives that I set out in my speeches in Florence and at Lancaster House.