The Liverpool forward has been barred from all football-related activity for four months, banned for nine competitive international matches and hit with an €80,000 (£64,000) fine.
Suarez had previously denied biting the defender, instead insisting his face "hit against the player, leaving a small bruise ... and a strong pain in my teeth" but has now come clean.
In a message posted on his official Twitter page, Suarez wrote: "After several days of being at home with my family, I have had the opportunity to regain my calm [sic] and reflect about the reality of what occurred during the Italy-Uruguay match on 24 June 2014.
"Independant 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 bite in the collision he suffered with me. For this:
- I deeply regret what occurred.
- I apologize to Giorgio Chiellini and the entire football family.
- I vow to the public that there will never again be another incident like [in] Montevideo, 30th of June 2014."
Suarez was previously banned for seven matches in 2010 for biting PSV's Otman Bakkal, during his time at Ajax before being suspended for a further 10 games after biting Branislav Ivanovic while playing for Liverpool.
Chiellini, himself, described the ban as "excessive" while the Uruguayan FA has informed Fifa that it will appeal against the ban, though it remains to be seen if Suarez's apology will change their stance.
The defender soon responded to his biter's message, accepting his contrition and hoping for a reduction to his suspension.
.@luis16suarez It's all forgotten. I hope FIFA will reduce your suspension.— Giorgio Chiellini (@chiellini) June 30, 2014