Britain's most senior police officer said the mayor, who took over as chair of the Metropolitan Police Authority yesterday, had told him he wanted a "change in leadership" at the top of the Met.
Sir Ian said: "Without the mayor's backing I do not think I can continue in the job."
Mr Johnson has pointedly failed to back Sir Ian since he took over at City Hall, and is due to chair his first meeting of the Metropolitan Police Authority on Monday.
The Scotland Yard chief said he had been asked to stay until 1 December to enable plans to be made for his successor's appointment.
Sir Ian defended his record at the top of the Met and said it was the duty of the Commissioner to lead the force "through good times and bad".
He said that the Home Secretary Jacqui Smith had "reluctantly but graciously" accepted his resignation.
"I am resigning not because of any failures of my service and not because the pressures of the office and the many stories that surround it are too much," he said.
"I am resigning in the best interests of the people of London and of the Metropolitan Police Service."
He said he had wanted to stay on until his contract ran out in February 2010.
"However, at a meeting yesterday the new mayor made clear, in a very pleasant and determined way, that he wished there to be a change of leadership at the Met."
Sir Ian will become the first serving Commissioner to resign before serving his term in more than a century, since James Munro, who quit in 1890 having failed to catch Jack the Ripper.
Ms Smith said she had accepted Sir Ian's resignation "with regret" and paid tribute to his work fighting crime in London and tackling terrorism across the country.
"Sir Ian can be proud of his contribution nationally and locally," she said. "He has transformed the police's capacity to prevent and deal with terrorism throughout Britain, including his leadership during terrorist outrages on London streets."
Deputy commissioner Sir Paul Stephenson will take over as acting commissioner when Sir Ian steps down, she added.
Sir Ian has faced criticism over his handling of a racism dispute with his most senior Asian officer, is at the centre of controversy of the death of Jean Charles de Menezes, and is under investigation over police contracts awarded to an associate.
The Daily Telegraph reported today that Boris Johnson, the London Mayor, was considering a vote of no confidence in Sir Ian, forcing the Home Secretary into a decision about his future.
Mr Johnson, who took over as chairman of the Metropolitan Police Authority yesterday, has called for the post of Met Commissioner to be directly accountable to City Hall.
The Daily Mail today printed allegations about Sir Ian's dealings. It reported that around £15,000 of public money was paid to Andy Miller to advise the Met chief when he took on the job.
It said that Mr Miller's company, Impact Plus, advised the Commissioner on communications strategy and leadership style. The paper also reported Scotland Yard paid the firm more than £3 million over six years.
Contracts awarded to the company are being examined by the Chief Inspector of Constabulary, Sir Ronnie Flanagan.
Sir Ian was already under pressure to quit after the Met was found guilty of breaching health and safety laws over the death of Jean Charles de Menezes.
The inquest into the innocent Brazilian's death at the hands of anti-terror police began last week and has once again turned attention onto the performance of the Met.
The Met is also at the centre of an unprecedented race row amid claims from senior officer Tarique Ghaffur that Sir Ian discriminated against him because of his race and religion.
The assistant commissioner was put on gardening leave after going public with his claims. Another senior officer, Commander Ali Dizaei, was suspended earlier this month by the Metropolitan Police Authority pending an investigation into his conduct.
As a result, the Metropolitan Black Police Association (MetBPA) has severed links with senior managers at the Met and accused the force of conducting a "sustained witch-hunt".
Sir Ian was appointed in February 2005 after being favourite to follow Sir John Stevens. He had been in the job a matter of months when London was hit by the July bombings.
He was seen as close to New Labour and as a moderniser who could help the Met respond to the charges of institutional racism made by the Macpherson Report after the death of Stephen Lawrence.
Educated at Christ Church college, Oxford, he was a detective in the Met before taking senior posts at the Thames Valley and Surrey forces.
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