Putting himself at odds with Jeremy Corbyn, he will say there is "no such thing as a good Brexit deal" and Labour must campaign unequivocally to remain.
Mr Corbyn has promised a further referendum on Brexit.
The Labour leader told the TUC conference on Tuesday that if Labour won the next election, it would offer a vote with a "credible Leave option" versus Remain.
Its election manifesto will promise to reach a better Brexit deal, but is not expected to commit to either Leave or Remain at that stage.
Mr Corbyn met trade union leaders on Tuesday, who urged him to keep Leave on any ballot.
Labour manifesto to offer vote on Leave and Remain
Would a Labour government cancel Brexit?
Where do the parties stand on Brexit?
Mark Serwotka, the general secretary of the PCS union, said this was the "only common sense" position and the binary choice on offer in a referendum was a "huge gamble" which risked "perpetuating" existing political divisions.
"I think Tom Watson's intervention is irresponsible and not what Labour communities need," he told the BBC's Newsnight.
'Provide a home'
But former Labour leadership contender Owen Smith said Mr Watson was speaking for "the majority of Labour members and Labour voters", and that the party "should be clearing the Brexit issue off the table before we get to an election".
Shadow Brexit secretary Sir Keir Starmer said the party was "very united" around the need for a referendum - despite the apparent difference in approach between the two men at the top.
He added: "There's a good discussion going on... we're not shutting down discussion in our party."
There is a way to get a Brexit deal, PM insists
Labour's hunt for Brexit 'reconciliation'
The Conservatives said Mr Watson had made it clear he wanted to "cancel" the 2016 Brexit referendum result.
"Only Boris Johnson and the Conservatives will deliver Brexit by 31 October, no ifs or buts, so we can move on and focus on the issues that matter to people," said its party chair James Cleverly.
BBC Newsnight political editor Nick Watt said he believed Mr Corbyn's aim was to "provide a home" for both Leave and Remain supporters at the next election but he could be forced to allow colleagues to campaign on both sides in the event of another referendum.
Mr Watson and other senior Labour figures, including Sir Keir, have already said they plan to campaign to stay in the EU in any circumstances.
Labour has voted twice against Boris Johnson's plans for a poll on 15 October.
The party's leadership has insisted it is eager for an election after the risk of a no-deal Brexit on 31 October has been ruled out.
In a speech in London, Mr Watson will say that while an autumn general election seems inevitable given Boris Johnson's loss of control in Parliament "that does not make it desirable".
"Elections should never be single issue campaigns," he will say, suggesting vital issues such as the future of the NHS, economic inequality and crime will be "drowned out" by the prime minister's "do or die" Brexit message.
"The only way to break the Brexit deadlock once and for all is a public vote in a referendum," he will say. "A general election might well fail to solve this Brexit chaos."
In the event of another general election in the coming months, Mr Watson says Labour must be "crystal clear" about where it stands on Brexit if it wants to get a hearing for the rest of its domestic policy agenda.
"There is no such thing as a good Brexit deal, which is why I believe we should advocate for Remain.
"That is what the overwhelming majority of Labour Party members, MPs and trade unions believe."
The Liberal Democrats, who pushed Labour into third place in May's European elections with a strident anti-Brexit message, are pushing for Brexit to be stopped in its tracks by revoking Article 50 - the legal process for the UK's departure.
While stopping short of calling for that himself, Mr Watson will say it is not too late for Labour to "win back" Remain voters.
"My experience on the doorstep tells me most of those who've deserted us over our Brexit policy did so with deep regret and would greatly prefer to come back," he will add.
"They just want us to take an unequivocal position that whatever happens we'll fight to remain, and to sound like we mean it."
Mr Watson will say that, though "very difficult", he and many others "respected the result of the 2016 referendum for a long time".
But, he will add: "There eventually comes a point when circumstances are so changed, when so much new information has emerged that we didn't have in 2016, when so many people feel differently to how they felt then, that you have to say, no... the only proper way to proceed in such circumstances is to consult the people again."
Another Labour MP, Gareth Snell - one of a group of MPs in the party wanting to bring back an amended version of Theresa May's original withdrawal agreement - said the "numbers simply don't exist" in Parliament to approve a further referendum.
He told Today: "The public have no appetite for a second referendum. The doors I knock every week… [voters] are not telling me they want to go back to the divisive referendum [but] they want a decision on this process to be taken as soon as possible."