The move sees Fabregas reunite with his former Arsenal team-mate Thierry Henry.
In two spells in English football, Fabregas made 501 appearances.
And the Spanish midfielder could make his debut this weekend against Marseille for struggling Monaco.
Chelsea said in a statement: “Cesc Fabregas has today completed a permanent transfer to Monaco.
“The midfielder’s switch to the Ligue 1 club brings the curtain down on his four-and-a-half year Chelsea career, a period in which he won four major trophies, including two Premier League titles.
“The Spaniard made 198 appearances for Chelsea, scoring 22 goals.
“We thank Cesc for his wonderful service and wish him the very best of luck for the next chapter in what has been a fantastic career.”
Fabregas won the Premier League twice, an FA Cup and the League Cup in his time at Chelsea.
And he said his goodbyes to the Chelsea fans and team-mates in their FA Cup win over Nottingham Forest on Saturday.
He seemed set to complete his move to Monaco at the beginning of the week but the deal was blocked by Chelsea as they were waiting for their £10million valuation to be met and wanted a replacement for the Spaniard before letting him leave.
Fabregas’ exit suggests Chelsea are close to finalising a deal for a new midfielder to take the 31-year-old’s place in the squad.
Fabregas said: “It is a great pleasure to join AS Monaco, a new project for me.
“The group is of quality with young players and a young coach. I’m here to help the team, I’m looking forward to starting, we have a great match to play in Marseille on Sunday.
“I am very excited.”
Monaco vice president Vadim Vasilyev added: “We are very pleased to welcome to AS Monaco Cesc Fabregas, a world-class player and a great professional, whose arrival demonstrates the ambition of the club.
“This is obviously a very good technical reinforcement for the team but we are convinced that his experience at the highest level will bring a lot to our players on and off the field.”