Mr Khan, who had previously said he would not take sides in the leadership contest, said he was now backing Owen Smith as Labour was “extremely unlikely” to secure a return to power under Mr Corbyn.
In a scathing article for The Observer, Mr Khan said the Labour leader had lost the confidence of MPs at Westminster and failed to win the “trust and respect” of the voters.
He also bitterly denounced Mr Corbyn’s performance in the EU referendum campaign, saying that he had to take his share of the blame for the vote to leave.
Mr Khan’s success in regaining the capital for Labour was one of the few bright spots for the party in an otherwise disappointing set of elections last May and his support for Mr Smith will be seen as a huge boost for the former shadow work and pensions secretary.
In his article, Mr Khan said while he considered Mr Corbyn to be a “principled Labour man” and did not regret nominating him for the leadership last year, he had since shown that he did not have the qualities needed to take them to success.
“By every available measure, if Jeremy remains as leader, Labour is extremely unlikely to win the next general election,” he wrote.
“The hopes of the members who have joined our party would be dashed again. Jeremy has already proved that he is unable to organise an effective team, and has failed to win the trust and respect of the British people.
“Jeremy’s personal ratings are the worst of any opposition leader on record - and the Labour party is suffering badly as a result. He has lost the confidence of more than 80% of Labour’s MPs in Parliament - and I am afraid we simply cannot afford to go on like this.”
Woundingly for Mr Corbyn, he echoed accusations that his lacklustre campaigning in the EU referendum had cost support for the Remain camp.
“Throughout the campaign and aftermath, Jeremy failed to show the leadership we desperately needed,” he said.
“His position on EU membership was never clear - and voters didn’t believe him. A third of Labour voters said they didn’t know where the party stood on the referendum just a week before polling day.
“And you can’t just blame a ‘hostile media’ and let Jeremy and his team off the hook. I know from my own election - up against a nasty and divisive Tory campaign - that, if we are strong and clear enough in our convictions, the message will get through to the public.
“That’s a test that Jeremy totally failed in the EU referendum. Why would things be different in a general election?”
With the first ballot papers due to go out this week to the 500,000 Labour Party members whose votes will decide the contest, Mr Smith - who is widely thought to be trailing in the contest - warmly welcomed the London mayor’s support.
“Sadiq ran a fantastic campaign to win power for Labour in London this year, securing a huge mandate from party members and the electorate,” he said.
“He showed that a vision of hope and optimism can win, if it’s backed up with a credible plan to deliver real meaningful change for people’s lives. Since that election we have already seen what a difference Labour can make when we hold power.”