Suarez was handed a four-month ban from all football-related activity and suspended for nine international matches after sinking his teeth into Chiellini's shoulder in Uruguay's final group match in Brazil last Tuesday.
The Liverpool striker, who has twice bitten opponents in the past, initially denied wrongdoing in a statement to FIFA and Uruguay's coach, Oscar Tabarez, accused the English-speaking media of blowing the incident out of proportion.
However, a statement from Suarez on Monday saw the 27-year-old admit his guilt and promise never to bite another player again.
"After several days of being home with my family, I have had the opportunity to regain my calm and reflect about the reality of what occurred during the Italy-Uruguay match on 24 June 2014," read the statement.
"Independent from the fallout and the contradicting declarations that have surfaced during these past days, all of which have been without the intention of interefering 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 (this)."
Suarez's apology comes after Uruguay were knocked out of the World Cup, courtesy of a 2-0 defeat to Colombia on Saturday.
The disgraced attacker had twice received lengthy suspensions at club level for biting prior to his most recent transgression.
He bit PSV Eindhoven midfielder Otman Bakkal during his time in Holland with Ajax in 2010, and then did likewise to Chelsea defender Branislav Ivanovic in a Premier League match last year.
Chiellini, Suarez's latest victim, has labelled FIFA's four-month ban as "excessive" but it remains to be seen whether it will be reduced, with the Uruguayan Football Association (AUF) having confirmed their intention to appeal.
