The controversial singer was asked to exit the ITV singing competition after breaking a 'golden rule'.
In a statement, 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 has issued an apology to his mentor Gary Barlow, his fans and his fellow contestants.
"I'd like to apologise to Gary, my fellow contestants and everyone who has voted for me, but, as of today (Tuesday, November 8), I will no longer be in The X Factor," he said.
"My life during the show has gone out of control and my behaviour off stage has over-stepped 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."
The 18-year-old, who has become notorious for his hard-partying lifestyle, is believed to have been asked to leave the X Factor house this morning.
Cocozza is currently at the centre of two Ofcom investigations, amid accusations that he swore on air and that his on-screen antics have glamorised the misuse of alcohol.
An announcement will be made tomorrow (Wednesday, November 9) on how Cocozza's departure will alter the format of the show, following calls for previously-axed contestants to return.