Mr Watson said it was clear the threat was real after a recording emerged of the founder of Momentum - the grassroots activists group which helped propel Mr Corbyn to the leadership - discussing the prospects of gaining Unite's backing.
Jon Lansman was said to have told supporters he expected the union - together with the Communication Workers Union (CWU) - to affiliate to Momentum if Mr McCluskey wins his battle for re-election as Unite general secretary.
In a series of angry Twitter exchanges, Mr Watson warned Mr Lansman: "You've revealed your plan. If you succeed you will destroy the Labour Party as an electoral force. So you have to be stopped."
However Mr Lansman, a long-time ally of Mr Corbyn, hit back, saying: "For 20 years the left was denied a voice. We will deny a voice to no-one. We face big challenges & we need our mass membership to win again."
The row erupted after The Observer obtained a tape of Mr Lansman's remarks, which were said to have been secretly recorded at a meeting of a newly-formed Momentum branch in Richmond, south west London, earlier this month.
He is quoted as saying: "Assuming that Len McCluskey wins the general secretaryship, which I think he will, Unite will affiliate to Momentum and will fully participate in Momentum, as will the CWU."
He went on to tell activists it was "absolutely crucial" that they secured a change to the party's rules to ensure that whenever Mr Corbyn stands down, they are able to get a candidate on to the ballot paper to succeed him.
Currently, a candidate must obtain the support of 15% of Labour MPs and MEPs in order to stand - a threshold a new left wing contender is unlikely to be able to meet.
Mr Watson said it was "a matter of great concern" that the Unite leadership appeared to be entering into a private agreement "to fund a political faction that is apparently planning to take control of the Labour party".
"I warned last year of entryism and no one can now doubt that threat is a real one," he said.
"For Unite to affiliate to Momentum it would require the approval of its executive committee. I hope Len McCluskey hasn't made promises without clearing them through the democratic structures of our union."
A Unite spokesman told The Observer that the general secretary could not make such a decision, adding: "Affiliation to Momentum is a matter for our executive council alone and no discussion on the matter is scheduled."
Momentum insisted there were no current plans for Unite to affiliate and said that it had not received any funds from them.
A spokesman said Mr Lansman had been speaking in "an aspirational manner" about the possibility of Unite and the CWU affiliating to Momentum.
However the disclosure looks set to reignite tensions between moderate Labour MPs and Mr Corbyn's left wing supporters which led to last year's failed coup attempt against the Labour leader.
Gerard Coyne, who is standing against Mr McCluskey as general secretary, said: "I have been warning for weeks that Len was trying to act as puppet master to Jeremy Corbyn. Now the evidence is clear for all to see."