"I would be wrong to allow my poor choice of words to detract from my colleagues' important reporting, so today I am resigning from Breitbart, effective immediately. This decision is mine alone," he added.
The publication added: "Milo Yiannopoulos' bold voice has sparked much-needed debate on important cultural topics confronting universities, the LGBTQ community, the press, and the tech industry."
It said Yiannopoulos decided to resign Tuesday morning and "we accepted his resignation".
As recently as last week, Breitbart editor Alexander Marlow called Yiannopoulos "the No. 1 free speech warrior of his generation in America at the moment" in an interview.
But Yiannopoulos' views on paedophilia apparently went too far even for Breitbart.
On his SiriusXM satellite radio programme, Marlow called Yiannopoulos' comments "indefensible" and "appalling".
"It's all very upsetting and something we take very seriously at Breitbart," but he made no comment about his future with the site.
Breitbart was under pressure from its own staff to take action against Yiannopoulos, 32. They had threatened an internal revolt if he wasn't fired or disciplined, according to people familiar with the discussions.
In a video interview early last year, Yiannopoulos bantered with the hosts of a podcast called The Drunken Peasants for nearly three hours. As the lengthy discussion veered into paedophilia, he condoned sexual relations with boys as young as 13 and joked about a sexual encounter he said he had with a Catholic priest as a teenager.
"You're misunderstanding what paedophilia means," he told the hosts. "Paedophilia is not a sexual attraction to somebody 13 years old who is sexually mature. Paedophilia is attraction to children who have not reached puberty."
He adds that consent by minors is "arbitrary and oppressive".
A group called the Reagan Battalion was among those calling attention to the interview to highlight its opposition to Yiannopoulos' speaking role at the upcoming Conservative Political Action Conference (CPac) in the Washington area.
The emergence of the video over the weekend triggered a cascade of adverse consequences for Yiannopoulos.
First, CPac's organiser, the American Conservative Union, rescinded its invitation to him as a conference speaker. The group's chairman said the organisation found Yiannopoulos' comments "disturbing" and the video "offensive".
Then Simon & Schuster cancelled an agreement to publish Yiannopoulos' forthcoming memoir, Dangerous, for which it paid him a US$250,000 ($248,000) advance. The publisher said it decided to cancel the book, which had drawn protests before the paedophilia flap arose, "after careful consideration".
Finally, about a half-dozen Breitbart employees told Marlow they would quit in protest if Yiannopoulos wasn't fired or disciplined, according to people familiar with the discussions who weren't authorised to comment publicly. Breitbart hasn't made any public comments since the issue arose.
Yiannopoulos, meanwhile, defended himself on Facebook on Sunday and Monday as the tide of controversy rose.
"I do not support paedophilia. Period," he wrote. "It is a vile and disgusting crime, perhaps the very worst. There are selectively edited videos doing the rounds, as part of a coordinated effort to discredit me from establishment Republicans, that suggest I am soft on the subject."
In an update Monday, he wrote: "I'm partly to blame. My own experiences as a victim led me to believe I could say anything I wanted to on this subject, no matter how outrageous. But I understand that my usual blend of British sarcasm, provocation and gallows humour might have come across as flippancy, a lack of care for other victims or, worse, 'advocacy'. I deeply regret that. People deal with things from their past in different ways."
He added, "I am certainly guilty of imprecise language, which I regret."
Yiannopoulos' speaking tour has sparked protests on college campuses for the past year, including one this month at the University of California at Berkeley that turned violent. In reaction, Trump threatened on Twitter to cut off federal funds to the school if it "does not allow free speech and practises violence on innocent people with a different point of view".
