The pro-Trump author had been due to talk about immigration on Thursday.
On 19 April, school administrators said the risk of violent protests meant they could not provide a safe venue.
Ms Coulter, who had originally vowed to visit the campus anyway, changed her mind after the event's organisers withdrew their support.
The Berkeley campus has witnessed destructive protests in recent months - not least over a planned appearance by alt-right poster-boy and outspoken Trump supporter Milo Yiannopoulos.
Rather than cancelling Ms Coulter's speech altogether, university authorities had asked her to hold it next week and at an earlier time, when the risk of clashes was lower.
The organisers of the event, the Young America's Foundation (YAF) and Berkeley College Republicans, then said they would sue the university.
The lawsuit claimed that Berkeley administrators were trying to "burden or ban" events "involving the expression of conservative viewpoints".
However, the YAF backtracked late on Tuesday, saying it could no longer sponsor the talk.
"Young America's Foundation will not jeopardise the safety of its staff or students," the group said. "Berkeley should be ashamed for creating this hostile atmosphere."
Ms Coulter, whose 2015 book is titled Adios, America!: The Left's Plan to Turn Our Country Into a Third World Hellhole, tweeted that free speech had been "crushed by thugs".
"Everyone who should believe in free speech fought against it or ran away," she said.
Ms Coulter has said the US is being "overwhelmed" by immigration. She was due to speak against it on Thursday.
Berkeley's chancellor wrote to students saying the university "did not cancel the Coulter event and has never prohibited Ms Coulter from coming on campus".
Chancellor Nicholas Dirks said the only reason she could not speak on Thursday was because the venue available was not safe; it could not be cordoned off, he said, and had floor-to-ceiling glass.
US conservative commentator Ann Coulter has cancelled a speech at the University of California, Berkeley, after a bitter free-speech row.