The Labour leader said he would serve as PM on a “strictly time-limited” basis so that he could delay Brexit past the October 31 deadline and call a general election.
Mr Corbyn asked Westminster's opposition leaders and key Tory rebels to support a no-confidence vote against Boris Johnson he plans to seek at the "earliest opportunity when we can be confident of success”.
However, his plans have already stalled after opposition leaders came out to say they would never make Mr Corbyn the Prime Minister, while Downing Street criticised him for planning to "overrule the referendum”.
Mr Johnson had warned earlier on Wednesday that the chances of a no-deal were becoming increasingly likely as he sticks to his "do or die" commitment to leave the EU by the current deadline.
What does Corbyn suggest?
In a letter, Mr Corbyn wrote: "This Government has no mandate for no-deal, and the 2016 EU referendum provided no mandate for no-deal.
"I therefore intend to table a vote of no confidence at the earliest opportunity when we can be confident of success.
"Following a successful vote of no confidence in the Government, I would then, as Leader of the Opposition, seek the confidence of the house for a strictly time-limited temporary government with the aim of calling a general election, and securing the necessary extension of Article 50 to do so.”
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Mr Corbyn said Labour would campaign in that election for a second referendum on EU membership with the option to Remain being available to voters.
He will hope that the promise of his government only being temporary will be enough to secure the support of his critics who otherwise want to halt a no-deal.
Opposition parties respond
Lib Dem leader Jo Swinson, who welcomed former Tory MP Sarah Wollaston into her fold on Wednesday, quickly scuppered some of those hopes by saying he was the wrong politician for the job.
"Jeremy Corbyn is not the person who is going to be able to build an even temporary majority in the House of Commons for this task - I would expect there are people in his own party and indeed the necessary Conservative backbenchers who would be unwilling to support him.
"It is a nonsense," she said.
"This letter is just more red lines that are about him and his position and is not a serious attempt to find the right solution and build a consensus to stop a no-deal Brexit.”
Shadow business secretary Rebecca Long-Bailey urged Ms Swinson to think again, telling Today: "What I would say is issue a plea to Jo Swinson particularly. I know that Jo wants to avoid a no-deal situation as we do, and we think this is the simplest and most democratic way of doing that.
"This isn't an issue about personalities and politics, it's not about implementing Labour policy, it's about avoiding a no-deal situation arising and ensuring that a general election is called, so ultimately the people can decide which government they want."
Anna Soubry, leader of the Independent Group for Change (formerly Change UK) said she could not support a government led by Jeremy Corbyn.
Ms Soubry told the Today programme: "I would not support a government of national unity that is led by Jeremy Corbyn for all manner of reasons.
"One, because I don't think it's genuine, secondly because it is not going to deliver a people's vote which is the only way through the chaos, and, of course, he doesn't command support or respect in his own political party, never mind across the Parliamentary divide."
However, SNP's Ian Blackford welcomed the Labour leader's letter and said the party would bring down the Tories in a no-confidence vote.
Plaid Cymru's Liz Saville Roberts also offered her cautious support, saying the party is open to a unity government regardless of who leads it, but that it must have "stopping Brexit" as its first priority.
Green Party MP Caroline Lucas, another recipient of the letter, also said she would back a no-confidence vote, but added that she wants Mr Corbyn to guarantee Labour's support for another MP to lead a temporary Government if his bid to govern fails.
How would Corbyn become PM?
Mr Corbyn could secure his proposed temporary administration by winning the support of the House of Commons after defeating Mr Johnson with the majority of MPs backing a vote of no confidence in the Government.
Then, as PM, he could table a motion for an early general election which would succeed with the support of two-thirds of the seats in the Commons, in the same fashion as Theresa May's doomed vote in 2017.
In an interview, Mr Corbyn said it was "hard" to put a time limit on his proposed caretaker leadership, but said it would have to endure Article 50 negotiations with the EU and a general election.
He suggested that he could lay down the no-confidence motion soon after the House returns from its summer recess on September 3.
Mr Corbyn ruled out an election pact with other opposition parties and appealed to MPs who do not support him but oppose no deal to "work with us" to "ensure there is no cliff-edge Brexit”.
A No 10 spokesman said: "There is a clear choice: either Jeremy Corbyn as prime minister who will overrule the referendum and wreck the economy, or Boris Johnson as Prime Minister who will respect the referendum and deliver more money for the NHS and more police on our streets."