"This is the right deal for the UK," she said after updating the cabinet on the text of a declaration on post-Brexit relations agreed Thursday.
Its text will be considered by an EU summit on Sunday alongside a draft divorce agreement struck last week.
"The British people want this to be settled," said May.
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"They want a good deal that sets us on course for a brighter future. That deal is within our grasp and I am determined to deliver it." Sunday's summit is meant to conclude nearly two years of complex and often acrimonious negotiations on how Britain and the European Union will function after their March 29 divorce.
The two final texts must then be approved by the UK and EU parliaments.
But Spain is threatening to vote against the agreements on Sunday because of a lingering dispute over the future status of Gibraltar.
Spain ceded the tiny island to Britain in 1713 but wants it returned.
Madrid is seeking to secure what it sees as its right to negotiate the future on Gibraltar with Britain on a bilateral basis after Brexit.
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This would give Spain an effective veto on Gibraltar's status. London has refused to budge. May signalled that she reaffirmed her position in a phone conversation late Wednesday with Spanish Prime Minister Pedro Sanchez.
"Last night I spoke to the Spanish prime minister, Pedro Sanchez, and I am confident that on Sunday we will be able to agree a deal that delivers for the whole UK family, including Gibraltar," she said.