Labour will oppose the package in Parliament and work with MPs from other parties to block a no-deal Brexit, Mr Corbyn said.
His comments came as former prime minister Tony Blair stepped up calls for a second referendum and suggested Labour was shifting towards that position.
As EU leaders signed off the package thrashed out by negotiators in Brussels, Mr Corbyn said: "This is a bad deal for the country.
"It is the result of a miserable failure of negotiation that leaves us with the worst of all worlds.
"It gives us less say over our future, and puts jobs and living standards at risk."
Shadow justice secretary Richard Burgon said: "Theresa May needs to is wake up and smell the coffee, ditch this deal and come back with something better."
Labour's policy is to reject the deal and call for a general election.
Challenged on BBC's Andrew Marr Show about the prospect of an election being unlikely, Mr Burgon said: "I think the age of the experts is over.
"The age of political certainty is over."
If there is not an election, Labour is keeping all options open including the possibility of another referendum on Brexit, although it has not specified what question would be asked.
Mr Burgon suggested another referendum may not even take place until after the UK has left the EU.
He said: "We don't know when such a referendum, if it takes place, would take place.
"Would it take place before we left the EU? Would it take place after we left the EU?"
Shadow Northern Ireland secretary Tony Lloyd told Sky News' Sophy Ridge on Sunday there could be a "coalition" behind a softer Brexit involving a customs union and close single market links.
"The British Parliament almost certainly has a coalition of the willing that would work round a customs union, work round single market standards of the kind that Labour has advocated but so have a broad swathe of other parties including a large number of Conservatives," he said.
Speculation about Labour's position on another referendum has been stoked by a Sunday Times report that shadow chancellor John McDonnell held talks with Tom Baldwin and Alastair Campbell, the former spin doctors to Ed Miliband and Mr Blair, who are now campaigning for a so-called People's Vote.
Mr Blair told the Andrew Marr Show "I think it's moving that way", adding: " I would be really surprised if the Labour Party doesn't end up in the position of supporting another vote, because there's no other proposition that can get through Parliament."
He suggested another referendum - with the choice between remaining in the EU and a "proper Brexit" of the kind sought by Leave campaigners such as Boris Johnson - would settle the issue.
"Both the Remain campaign and the Leave campaign should jointly agree that this vote is final, doesn't matter how marginal it is, it's final," he said.
"Once this is resolved then that's it for a generation."
He added that he thought Mrs May was "a decent person, frankly surrounded by a lot of pretty unreasonable ones" but "the deal's a dodo".
But former minister Caroline Flint hit out at Labour colleagues calling for another referendum.
It was an "11th hour attempt to overturn the result" of the 2016 referendum and would mean siding with Tory Brexiteers to reject Mrs May's deal - leaving the UK at risk of "crashing out" without a deal.
She warned "the consequences are dire" and another referendum would lead to the a "far-right resurgence, discord and distrust".
If the Prime Minister's deal is going to get through the Commons, she may be forced to rely on the votes of Labour MPs from Leave-supporting areas.
But Wigan's Lisa Nandy said it was "inconceivable" that she would back the deal, instead telling Sky News that Article 50 should be extended for a process of "dialogue and consensus" with the public.