The motion was thrashed out in a tense five hour meeting of Labour officials overnight after a day in which tensions on the Brexit issue threatened to run out of control.
Corbyn has so far tried to avoid the divisive subject, instead sticking to promoting a domestic social agenda that helped him upset the odds at last year's general election and strip May of her parliamentary majority.
More than 100 constituency parties have submitted motions calling for the issue to be put to a vote.
Mr McDonnell said a general election would be "the real People's Vote" on Brexit.
Speaking on BBC Radio 4's Today programme, .
"If it doesn't meet those tests, yes, we want a general election, but we will keep the option of a people's vote on the table just in case".
The motion which delegates will vote on whether to support states: "If we can not get a General Election Labour must support all options remaining on the table, including campaigning for a public vote".
Mr Watson supported the idea of being joined in the leadership team by a female deputy, as did numerous trade union members of the NEC.
"So if the people's party decide they want the people to have a final say on the deal, we have to respect the view of our members and we will go out and argue for it".
United States and China imposed fresh tariffs on each other’s goods
Ironically, the document was unveiled during the Mid-Autumn Festival period, a major holiday in China. It accused the United States of contradicting itself on trade policy and called for cooperation.
The close Corbyn ally dismissed the idea that the verdict from the 2016 national vote should be revisited.
"We're respecting the referendum". The people have decided against my wishes and my Union's wishes but they've decided'.
On Sunday, the campaign for a People's Vote said its supporters were pleased with "signs that the Labour leadership was listening to its membership".
Mr Corbyn, appearing earlier on Sunday on BBC1's Andrew Marr Show, has been asked whether he would feel obliged to respect a vote by delegates to support a second referendum.
'What comes out of conference I will adhere to. "Obviously I'm bound by the democracy of our party".
He added: 'That is what happens when you return the party to the members'. "It absolutely must include the right to remain in the European Union".
Mr Lammy shouted to the hundreds of people who marched through the city in support of the People's Vote campaign.
"I am not sure there is life left in Chequers", Morgan, chair of parliament's Treasury Select Committee and a former cabinet minister under May's predecessor, told Sky News.
He has always been a critic of the EU's free-trade policies and must also find a way to reconcile the traditional working-class wing of his party, who mostly voted for Brexit, and his own army of younger supporters that want to stay in the bloc. I think we should have this sort of system for leader as well.