"Following that ... she and I will meet to agree a timetable for the election of a new leader of the Conservative Party," Brady said.
May's 10 Downing St office said Brady spoke with the Prime Minister's agreement, and insisted May remained focused "on securing our departure from the EU" by getting backing for her EU divorce deal.
May's successor will be chosen by a party leadership contest in which any Conservative lawmaker can run. The winner will become party leader and prime minister without the need for a general election.
May survived a no-confidence vote among party colleagues in December, and under Conservative rules she can't face another challenge until a year has passed. Some lawmakers have been pressing for a change to those rules to allow a new vote on May's leadership as soon as June.
Pro-Brexit Conservatives are furious that Britain has not yet left the EU, almost three years after voters backed Brexit in a referendum. Many blame May for the impasse and want her replaced with a more staunchly pro-Brexit leader such as the former Foreign Secretary, Boris Johnson.
Johnson told a business event yesterday that "of course I'm going to go for it" when the contest to replace May as Conservative leader is formally launched. Several members of May's Cabinet have also started unofficial leadership campaigns.
May points out that she struck a divorce deal with the EU, but it has been rejected by Parliament three times, even by many of the same lawmakers who backed Brexit in the referendum.
May has said she will resign once a Brexit deal is approved and make way for a new leader to guide the UK through the next stage in the process, which will determine the country's future relationship with the EU.
The UK's departure from the EU, long set for March 29, has been delayed until October 31 while British politicians try to break the deadlock.
May plans to make a fourth attempt to get lawmakers' backing for Brexit terms by putting a withdrawal agreement bill to a vote in early June. She says that if it passes, Britain could leave the EU in July.
But it's unclear how the Government plans to persuade a majority of lawmakers to back May's EU divorce terms, since few legislators on either side of the Brexit divide seem prepared to change their positions.
Weeks of talks between the Government and Labour have failed to produce a compromise agreement.
"I'd have thought it was patently clear that if the Prime Minister's deal is put for a fourth time, if it's allowed, it will fail just as it has failed three times already," said Labour Brexit spokesman Keir Starmer.
- AP