The PM said the deal was the right one for the UK and "is within our grasp," so she was determined to deliver it.
The agreement was struck with the European Commission, May added, and it was up to the EU 27 to review it in the lead up to the special EU Council meeting on November 25.
Theresa May discussed the Gibraltar issue with the Spanish PM Pedro Sanchez on Wednesday evening.
"I am confident that on Sunday we will be able to agree a deal that delivers for the whole UK family, including Gibraltar" May said in her statement.
However, most recently, diplomatic sources have reportedly confirmed Spain has vowed to vote against the Brexit deal over Gibraltar
WATCH LIVE: PM @Theresa_May gives a statement on Brexit https://t.co/NB5lv7iplr
— UK Prime Minister (@10DowningStreet) November 22, 2018
Gibraltar First Minister Fabian Picardo has been reported to say on Thursday that Britain's overseas territory will be part of any Brexit agreement
Spain has threatened to vote down the proposed deal, objecting to the wording of the Article 184, which says the EU and the UK will seek to "negotiate rapidly the agreements governing their future relationship" between 29 March 2019 and December 2020.
According to the Spanish government, the statement is not clear on whether it covers the status of Gibraltar, a British overseas territory that's long been the bone of contention between London and Madrid.
Earlier this week, the German Chancellor Angela Merkel said she hoped for a positive outcome of EU27 negotiations and for a solution to the Gibraltar disagreement before the November 25 deadline.
READ MORE: We Know Spain Has Gibraltar Issues But We Will Uphold Brexit Deal — Merkel
European Council President Donald Tusk confirmed on Thursday a deal had been struck in principle ahead of the Sunday summit.
Theresa May has updated her Cabinet on the progress achieved and will be making a statement to the House of Commons Thursday afternoon.
