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 European Union divorce deal.
Here is how the drama could play out over the next few months. In the past it has taken months to complete but it could be speeded up in order to give the new leader more time to try to resolve the Brexit impasses before October 31.
May's hands have been tied, knowing that to make concessions to Labour would lead to fury in her divided party.
Blaenau Gwent Labour AM Alun Davies told the Senedd: "These chancers did not stand for election under any party label they are using today".
Mrs May has pledged to bring the EU Withdrawal Agreement Bill - the legislation known as WAB that would implement her deal - before the Commons for a crucial vote in the week of June 3. She has maintained that she will resign once a divorce deal is passed.
May points out that she struck a divorce deal with the European Union, but it has been rejected by Parliament three times, even by numerous same lawmakers who backed Brexit in the referendum.
UK Parliament has repeatedly said it does not want a no-deal Brexit. Those votes could happen as early as next week.
Under the process, MPs will whittle what looks to be a crowded field of candidates down to two - with ordinary Conservative members voting to decide the victor.
In a head-to-head run-off, Mr Johnson resoundingly beats Mr Raab by 59 points to 41, and beats every other contender by an even bigger margin. If the cross-party talks fail, move on to the next stage.
Parliament usually breaks for around six weeks over the summer.
"Cabinet ministers are competing to succeed you, the position of the government has become ever more unstable and its authority eroded", Corbyn wrote to May on Friday.
Labour can not even agree within its own senior ranks what its position is on Brexit - it was never going to agree with the Government!
Mr Johnson's chances of winning the Tory crown have soared amid signs that the party's support is haemorrhaging to Nigel Farage's Brexit Party. The victor will become party leader and prime minister of the United Kingdom without the need for a general election.
Johnson, the former mayor of London, has been one of May's most outspoken critics over Brexit and supports leaving the European Union without a deal, a scenario the government's own economic forecasts have warned would leave the British economy eight percent smaller by 2035.