The teenager had “broken competition rules”, according to producers of the show.
Cocozza admitted: “I no longer deserve my place in the show.”
His antics have already prompted an Ofcom investigation into the series. The young wannabe has been pictured on a string of nights out since finding fame in the contest.
He made an impact in the early stages when he boasted that the names of some of his many lovers were tattooed on his bottom.
He said yesterday that his life had “gone out of control” while taking part in the show.
As he left, he said sorry to his mentor, Gary Barlow, and fans who had been voting for him.
Many viewers were astonished that the singer remained in the competition following a below-par performance at the weekend.
Other acts were advising him to curb his behaviour to concentrate on the contest.
Andy Merry, of boyband The Risk, voted out on Sunday, said: “We’ve said to him ‘You’ve got a great opportunity here, just calm down a bit’.”
Cocozza said yesterday: “I’d like to apologise to Gary, my fellow contestants and everyone who has voted for me, but, as of today, I will no longer be in The X Factor.
“My life during the show has gone out of control and my behaviour off stage has overstepped the rules of the competition.
“I no longer deserve my place in the show, so I am therefore leaving. I would like to thank everyone who has supported me.”
A spokeswoman for The X Factor said: “Frankie is leaving the show today after breaking competition rules. He is going to take some time out before continuing his career as a singer.
“We wish him all the best for his future.”
Cocozza’s behaviour has led to two investigations by Ofcom into possible breaches of its programme code. It is looking into whether he fell foul of rules about swearing after he was seen to shout “f****** have it – get in there”, when he learned he was through to the next round on October 23. It is also looking into whether footage of him during a night out with friends may have breached the code’s rules on glamorising alcohol use.
It is the latest drama to engulf the show as it struggles to match audiences in previous years.
One group member walked out of the show, leaving The Risk to recruit a new member from an axed band. And judge Kelly Rowland left the country shortly after an on-air spat with fellow judge Tulisa Contostavlos. She then had to fire one of her singers by phone during a live results show.