The Spain international, now playing for Chelsea, had long been suspected as the culprit in October 2004 after Manchester United had beaten the Gunners 2-0 to end their 49-game unbeaten Premier League run.
On the upcoming episode of sports panel show A League Of Their Own, host James Corden asks Fabregas: "Tonight, can we finally put the case of the flying pizza to bed once and for all? Were you the culprit that threw the pizza?"
"Yes," replied Fabregas. "All of a sudden, I heard noises [from the tunnel] and I thought what's happening? So I go out with my slice of pizza and I saw Sol Campbell, Rio Ferdinand, Martin Keown... everyone pushing each other.
"I was like, I want to get in but I don't know how to and I threw... peeew... just threw it. Once I saw it was hitting, like, who it was hitting, which I didn't mean. I apologise Sir Alex, really didn't mean to do that!"
Arsenal finished second in the 2004-05 Premier League season, one place ahead of Man United, as Chelsea claimed the title.