After initially denying that he bit Chiellini, Suarez issued a carefully worded statement on Monday admitting his offence and remorse for his actions.
"After several days of being home with my family, I have had the opportunity to regain my calm and reflect on what occurred during the Italy-Uruguay match on 24 June," he said in a statement published on his Twitter account.
Suarez was banned for Uruguay's next nine competitive international matches and from any involvement in football for four months by FIFA after biting Chiellini in Uruguay's 1-0 Group D win over Italy.
"Independent from the fallout and the contradicting declarations that have surfaced during these past days, all of which have been without the intention of interfering with the good performance of my national team, the truth is that my colleague Giorgio Chiellini suffered the physical result of a bit in the collision he suffered with me," Suarez added in his statement.
"For this: I deeply regret what happened; I apologise to Giorgio Chiellini and the entire football family; I vow to the public that there will never again be another incident like."
Image: Luis Suarez and Giorgio Chiellini
Photograph: Matthias Hangst/Getty Images
Football World Cup: Best PHOTOS from group stage matches
Costa Rica beat Greece on penalties to make last eight debut
World Cup sidelights: Netherlands offered space trip if they take home trophy!
PHOTOS: Rodriguez brace powers Colombia into quarters
World Cup Player of the Day: Game-changer Robben does it again for the Dutch