In a major speech - nearly three years on since the referendum - he will say that being part of Europe is an "emotional issue", as he issues a renewed plea to the Labour leadership to fight for a future inside the bloc amid the danger of a no-deal Brexit.
Tomorrow, the shadow cabinet, including Mr Watson, will meet to debate Brexit in the wake of Labour's woeful performance at the European elections and mounting pressure on Mr Corbyn over the party's policy.
The Labour leader has so far resisted calls to wholeheartedly back a Final Say referendum, leaving open the door to the party negotiating its own Brexit deal should it return to government.
In the fallout of the European elections - being pushed into third place by the Liberal Democrats - Mr Corbyn said that any Brexit deal would have to be put to a "public vote", including the option of a general election.
Speaking ahead of Monday's shadow cabinet meeting, Mr Watson will say: "Our members are remain.Our values are remain. Our hearts are remain. We must bring the public back into this decision and we must argue strongly to remain in Europe."
"Our future doesn't need to be Brexit. We can change our future. But only if Labour makes the case for it – and we must."
In his speech on Europe at the Centre for European Reform, the deputy leader will also recount a recent conversation he had with Justin Welby, the Archbishop of Canterbury.
"Something he said to me resonated very deeply. He told me that our politicians need to learn to 'disagree well'. I think we all instinctively understand what he means by that," Mr Watson will say. "I will try to make the positive case for what I believe.
"In return, though, a plea. In the Labour movement there is a range of views on how to best serve our mission, our purpose and our people when it comes to the Brexit dilemma.
"It is right and reasonable that all voices are heard, that all positions are given a hearing. But we cannot go on dismissing one another's right to speak and questioning one another's motives and intentions."
Mr Watson's call came Lord John Kerr, one of the architects of Article 50 and the UK's former top diplomat, claimed that contenders in the Conservative leadership race were were presenting "unrealistic" and "fantasy" proposals for Brexit. "The unicorns are back, frolicking in the Tory forest," he said on Sunday.
His remarks coincided with the release of a dossier from the People's Vote campaign, claiming all the candidates vying for the Tory crown had their own "Brexit unicorns" on offer, including the renegotiation of the withdrawal agreement, and withholding the payment of the divorce bill with the EU.