He will reunite with former Arsenal team-mate and close friend Thierry Henry at Stade Louis II, with the Gunners' all-time top goalscorer taking his first steps in management after Leonardo Jardim was sacked in October.
Now 31, Fabregas eventually made the same move as Henry when he left the Emirates Stadium for Barcelona, but he returned to English football with Chelsea in 2014.
"It is a great pleasure to join Monaco, it is a new project for me".
"I'm looking forward to starting, we have a great match to play in Marseille on Sunday".
The former Marseille and Roma player was expected to put pen to paper on a move from Turkish club Antalyaspor, but Monaco announced earlier on Friday that he had failed a medical due to a calf problem.
Fabregas was previously Jorginho's deputy in the deepest midfield position, with the World Cup victor being the only other central player in our squad capable of dictating the play from that area of the pitch. "I am very excited".
"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, " Chelsea FC wrote.
Avoiding serious injury helped him to play around 650 club games and to score 121 goals - winning league titles with Barcelona and Chelsea and domestic Cup competitions with all three sides.
"We are very pleased to welcome Cesc Fabregas, a world-class player and a great professional, whose arrival demonstrates the ambition of the club", said Vadim Vasilyev, the club's vice president and general manager.
However, they have won just twice in nine league games since Henry's arrival and now languish in the relegation zone, five points from safety before the weekend's matches.