Several MPs and former prime minister Tony Blair had expressed outrage after Jon Lansman, founder of the Corbyn-supporting Momentum group, filed the motion with the National Executive Committee.
If successful, the deputy leader position would have been scrapped – ejecting Mr Watson out of the shadow cabinet.
Labour MP Wes Streeting wrote on Twitter: “Motion withdrawn, now that consequences of it going ahead have been made clear by MPs and unions. Labour conference opens with headlines about division and civil war.
“Excellent health, environment and workplace rights announcements drowned out. Shameful from Lansman and Momentum.”
The withdrawal came after Jeremy Corbyn sought to head off the attempt with a motion promising to review the position.
Arriving at conference in Brighton, Mr Corbyn said the NEC had met in a “happy and united mood”.
Asked if he backed Mr Watson, he said: “Tom Watson is the deputy leader of the party and I enjoy working with him.”
Mr Corbyn’s motion says: “The NEC commits to a review of the position of deputy leader and other positions in support of the leader, to increase democratic accountability, and ensure that they reflect the diversity of our society and to explore the scope for gender and other forms of diversity in these positions.
“The review should consider the scope for expanding the number of elected positions in support of the leader and ensuring the process for nomination and election for these positions is broadened and draws on every part of our movement.”
A Labour Party source said: “Jeremy Corbyn proposed that the motion not go to a vote and instead that there be a review of the position of deputy leader and other positions in support of the leader.
“This will consider how democratic accountability can be strengthened to give members a greater say, expanding the number of elected positions, and how diverse representation can be further improved. The NEC agreed to his proposal.”
Mr Lansman later added: “I welcome & fully support Jeremy’s proposal to review Tom Watson’s position. We need to make sure the deputy leader role is properly accountable to the membership while also unifying the party at conference. In my view, this review is absolutely the best way of doing that.”
While there were reports overnight that Mr Corbyn had not known about the motion, Labour MP Peter Kyle told Sky News that from the perspective of a member of the public, it was “inconceivable” that he would not have known.
He said: “It would be extraordinary if someone putting themselves forward to be prime minister didn’t know this was happening around them. If you lead the party, you are involved in big decisions.”
Before the Momentum motion was withdrawn, Mr Blair had warned: “A decision to abolish the post of deputy leader would be undemocratic, damaging and politically dangerous. To suggest it at this time shows a quite extraordinary level of destructive sectarianism.
“The Labour Party has always contained different views within it and the deputy leader’s position has been one way of accommodating such views.
“Getting rid of it would be a signal that such pluralism of views was coming to an end despite being cherished throughout Labour’s history.”
The chair of Labour’s National Executive Committee had ruled the motion should be thrown out.
Mr Watson told the BBC he found out about the motion while at a Chinese restaurant in Manchester on Friday night, as he could not get to the conference in Brighton until later because of childcare issues.
He made it clear Mr Corbyn could stop the motion.
Mr Watson recently called for a new Brexit referendum to be held before a general election.
On the other hand, Mr Corbyn says Labour will offer people a second referendum only after an election.
Earlier, Mr Watson called the move a “straight sectarian attack on a broad church party”.
He added: “It’s moving us into a different kind of institution where pluralism isn’t tolerated.”
Dawn Butler, shadow women and equalities minister, failed to explicitly back Mr Watson in his cabinet role.
When asked if Mr Watson should be the deputy leader, she told Sky News: “Of course I think Tom should be in the party.
“He is there to support the leader. We are a broad church, people have different views and express those in different ways.
“You’re asking me to interfere with the NEC process.”
Ms Butler admitted the motion had come as a surprise to her but denied that it indicated the Labour Party was ripping itself apart.
She said: “If we keep going down the speculation road we are going to go deeper and deeper and create an augmented reality vision of the party. It’s important that people understand the process, otherwise they will get carried away.”
Ms Butler told the BBC she has her own “frustrations with Tom too”, saying “I haven’t seen him at a shadow cabinet meeting for a while.”
Earlier this month, Mr Watson said his party must “unambiguously and unequivocally back Remain”, but Mr Corbyn has always been more cautious about this approach.
Several Labour MPs criticised the move against Mr Watson and the committee of the Parliamentary Labour Party wrote to the NEC, saying the motion was “counterproductive” and “entirely factional”.
The party “should be about putting forward a strong, unified message and showcasing the policies that will win that election”, said Justin Madders, a Labour MP.
Former party leader Ed Miliband said those responsible had “taken leave of their senses”.
Ben Bradshaw, a former cabinet minister, called it “totally f****** insane”.
Unison general secretary Dave Prentis tweeted: “Our sole focus at Labour conference this week should be on taking the fight to Boris Johnson. What we need at this time is unity and a focus on winning the upcoming election.
“Anything else is a betrayal of Unison members and working people everywhere who are relying on us.”
Labour was already facing a battle over its Brexit policy as conference began, with activists mounting a campaign for the party to back a Remain stance, but Mr Corbyn hinting he would stay neutral during a second referendum.
He denied his policy on leaving the EU is a “muddle” saying leadership comes from listening.
Scottish and Welsh Labour both back remain and members in Northern Ireland have submitted a motion to conference that “any form of Brexit threatens jobs, workers’ rights, migrants, the NHS, public services and the environment”.
More than 90 motions on Brexit have been submitted to conference, most of them supporting remain.