But a move for midfielder William Vainqueur from Turkish club Antalyaspor fell through, after he failed a medical due to a calf problem.
The 31-year-old Fabregas is young enough to be considered a big signing for Monaco and he could have a major bearing on the club's chances of staying up.
Fabregas while with Chelsea helped the west London outfit win two Premier League titles, the FA Cup and the League Cup. I'm here to help the team. "I am very excited".
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.
Fabregas bade an emotional farewell to Stamford Bridge at the end of last week's FA Cup win over Nottingham Forest.
"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 said in a statement.
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".
There will be little time for the former Barcelona midfielder to enjoy the Principality, as Monaco now sit second from last in Ligue 1.
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