The Labour leader made the comments during his main speech at his party conference in Liverpool on Tuesday.
He lambasted the PM's Chequers deal and said if the Tories could not forge a deal with Brussels also acceptable to parliament, they should make way or Labour.
He said: "If you deliver a Brexit deal that includes a customs union and no hard border in Ireland, if you protect jobs, people's rights at work and environmental standards, then we will support that sensible deal.
"But if you can't negotiate that deal, then you need to make way for a party that can – and will.
PA
EASY: Corbyn said Labour would vote against the Chequers plan or whatever is left of it
(Pic: PA)
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"We must take our message to every town, city and village. United and ready to win, ready to govern as we were in 1945, 1964 and 1997.
"So that when we meet this time next year let it be as a Labour government. Investing in Britain after years of austerity and neglect and bringing our country together after a decade of division."
He earlier said Mrs May had left the country staring at a choice between no deal or bad deal."
Labour's stance will be to vote down the Chequers deal and oppose leaving with no agreement, he confirmed.
PA
CAPTIVE: Former deputy PM John Prescott watches Corbyn's speech
(Pic: PA)
He told members: "Labour respects the decision of the British people in the referendum. But no one can respect the conduct of the government since that vote took place.
"We all hoped that the peoples decision would be followed by effective and responsible negotiations that would protect living standards and jobs.
"Instead, the main negotiations have taken place between different factions of the Tory party and the only job this government is fighting for is the Prime Ministers."
Mr Corbyn did say he would back a "sensible deal" negotiated by Mrs May, which featured a customs union and no hard border with Ireland.
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At the close of his 59-minute speech, Mr Corbyn said: "We must take our message to every town, city and village.
"United and ready to win, ready to govern as we were in 1945, 1964 and 1997. So that when we meet this time next year let it be as a Labour government."
He added: "Let every constituency, every community know Labour is ready: Confident in our ideas, clear in our plans, committed to rebuild Britain."
EU negotiator Michel Barnier confirmed today he was set to meet Corbyn on Wednesday.
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