Video report by ITV News Correspondent Romilly Weeks
Labour members will vote on a Brexit motion stating the party should "support all options remaining on the table, including campaigning for a public vote" if it cannot force a general election.
Delegates agreed the wording of the motion, which will be put to a vote at the party's conference in Liverpool on Tuesday, after a marathon late-night meeting.
Labour leader Jeremy Corbyn has previously resisted calls to back a second Brexit referendum, but has accepted he would be "bound" by any decision made at the conference.
ITV News Political Editor Robert Peston tweeted that Labour's announcement marked a "big shift", but added that any referendum would only be on the outcome of the Government's Brexit deal, rather than another vote on whether to stay in or leave the EU.
Speaking to ITV News, shadow Brexit secretary Keir Starmer said that Labour's stance on a People's Vote was "deliberately left wide" in talks with delegates.
He added that "nothing was taken off the table" in regards to remain still being an option should there be a second referendum, seemingly contradicting John McDonnell's comments, in which he said that the party "respected" the June 2016 referendum result.
"Well I think in the room last night and everybody realises that we don't quite know what's going to come next," Mr Starmer said.
"For example, we don't know whether there's going to be a deal or no deal. So we're going to have to confront the options as they arise."
In further comments to ITV News, Mr McDonnell said that any second referendum would not be another vote on whether the UK should leave the EU or not, but on the terms of any deal negotiated by the Government.
However, this was strongly refuted by Labour MP Ben Bradshaw, who told Political Correspondent Paul Brand that the shadow chancellor "can't have read the motion properly" and that what Mr McDonnell has said was "a nonsense", since the party decided to keep open the option of remaining in the EU.
The Exeter MP added that it could not be a choice between "a bad Tory deal and a no deal", adding that "of course the option of staying in [the EU] would have to be on the ballot paper".
Mr McDonnell also told ITV News that preferable to a referendum on the Government's deal would be a General Election - "the real People's Vote" on Brexit.
The Hayes and Harlington MP said this would allow all the issues around Brexit deal to be "thoroughly debated", allowing the public to then "choose the team".
He added that the Government had "negotiated recklessly" with the EU so far, so they should "let Labour take over" and negotiate a deal which would "protect jobs and the economy".
On Sunday, Labour's deputy leader Tom Watson confirmed to ITV News that Labour would back a second referendum on Brexit if members back it at the party's conference in Liverpool.
"Jeremy and I are keen that we have a proper debate on Brexit and of course we'll respect the decisions they make at the end of conference," Mr Watson said.
Asked by Brand if that meant the leadership would adopt a new stance if members back another public vote at conference, he said: "Of course we have to listen to our membership and it will be built into our policy positions going forward."
However, the proposal has not been met by enthusiasm from all Labour members, prominent MP David Lammy said it would be "farcical" to offer a referendum between "no deal or a bad deal".
The referendum "absolutely must include the right to remain in the EU", he said, an option which has been discounted by the Party's top brass.
These Labour supporters tell us why they want a second vote
The leadership comments came as a poll found 86% of Labour members think voters should have the final say on Brexit.
Labour politicians joined thousands in a march through Liverpool on Sunday demanding a so-called People’s Vote.
And more than 100 constituency parties have submitted motions calling for the issue to be put to a vote.
Many activists believe that with Theresa May’s plans in disarray following the rejection of her Chequers proposals by EU leaders in Salzburg, the time is now right for Labour to throw its weight behind a fresh ballot.
A YouGov survey of more than 1,000 Labour members found 86% support a referendum on the outcome of Brexit talks, against just 8% who oppose it.