Sadiq Khan says he can guarantee Crossrail will open next year, and delays will not push the railway back to 2022.
The Mayor spoke exclusively to the BBC Local Democracy Service as Crossrail bosses announced plans to open the central section of the line by summer 2021.
The railway will link Reading, Heathrow, and Essex to central London, with a branch to the south east of the city.
It was due to open in December 2018, but has faced a series of delays.
Mr Khan said: “Because of the huge problems in 2018 and my anger at the delay in Crossrail being so late, we’ve got rid of the previous chair.”
Tony Meggs became chairman of Crossrail in January last year, and Mark Wild took over as chief executive.
The Mayor said: “I’ve got confidence in them, and they’ve announced today, as the result of a meeting yesterday, that next summer the central section of Crossrail should open up.”
Mr Khan said the new line would “transform public transport in London” and it was “really important” that investment continued.
The project could be more than £3billion over budget, with up to £650million of overspend still not secured.
Originally set to cost £14.8bn, the bill for Crossrail will now be £18bn or more.
In an apparent attempt to distance himself from problems on the line, Mr Khan said: “Crossrail was set up as an autonomous body and so although the Department for Transport and Transport for London are sponsors, we have very little say over what happens with Crossrail.”
The Mayor has previously been criticised for failing to spot problems with the project as they first arose.
Earlier this week, Transport for London (TfL) Commissioner Mike Brown said he was planning for an opening date as late as autumn next year – meaning the rail link would be almost three years late.
But Crossrail bosses insisted today that the central part of the line would open by May next year – and the whole project would be complete by May 2022.
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On Monday, Mr Brown said the eastern branch to Shenfield in Essex could open as late as December 2022.
The Crossrail team are currently developing essential software that will be used to run trains along the line.
Leaders say this will be finished by autumn this year. They can then start test running trains along the tracks.
This trail running will be followed by a final stage of testing when passengers will be invited onto the line.
The timetable for completion remains tight, as trial running of trains will take between 9 and 12 months.
Conservative London Assembly member Gareth Bacon – who questioned TfL about Crossrail at the Assembly’s budget committee on Monday – said he was sceptical about the Mayor’s promise today.
He said: “On the face of it this is better news than we heard at the beginning of this week.
“However, we’ve had so many promises broken that I’ll believe it when I see it.”
He added: “Early in the Mayor’s term he was keen to take credit for everything that was happening with Crossrail.
“But when things started to go badly wrong he started speaking about the Department for Transport and TfL being joint sponsors.
“Crossrail is a wholly owned subsidiary of TfL and the head of TfL is the Mayor.
“The idea that he is somehow divorced from Crossrail is complete nonsense.”
Crossrail chief executive Mark Wild said his team is doing “everything we can” to open the line to passengers.
He said: “We have a comprehensive plan to complete the Elizabeth line and the milestones we must hit during 2020, including the testing of the signalling and train systems and safety assurance – but there are no shortcuts to delivery of this hugely complex railway.
“Our latest assessment is that Elizabeth line services through central London will commence in summer 2021 but we are aiming to open the railway as soon as we can.”