The Spanish International leaves English football after 501 matches.
Fabregas had on Saturday left the pitch in tears after making his final appearance for the Blues in the FA Cup win against Nottingham Forest
He started just one league game under Maurizio Sarri this season.
“It is a great pleasure to join AS Monaco, a new project for me,” Fabregas said in a statement
“The group is quality with young players and a young coach. I’m here to help the team.
“I am looking forward to starting, we have a great match to play in Marsielle on Sunday. I am very excited.”
Reacting to his exit, the club said “There is no doubt Fabregas’s place in the Chelsea history books is assured given his achievements over the past four-and-a-half seasons.
“Big goals and outstanding moments of quality, all backed up by the ultimate aim, which is to be part of a successful, trophy-winning team.
“Fabregas departs having helped the club achieve great success, as well as providing our supporters with some wonderful memories.”
Fabregas joined Chelsea from Barcelona in 2014, scoring 22 goals and laid on 57 assists during his 198 appearances in West London
