The 31-year-old signed a three-and-a-half-year-deal with the French club.
In a lengthy statement on their website, Chelsea paid tribute to Fabregas, who won two Premier League titles as well as both FA Cup and League Cup winners' medals during his time with the club.
The Spaniard left Stamford Bridge after 501 appearances in English football to join up with former Arsenal team-mate Henry to help Monaco beat the drop. Have your say in the comment section below.
Cesc Fabregas has agreed to a €10 million ($11.5 million) transfer from Chelsea to Monaco.
Fabregas described the move as "a new project" and a "great honour".
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Cesc Fabregas played 303 times for Arsenal between 2003 and 2011, helping the club win the 2005 FA Cup.
Monaco, managed by Fabregas's former Arsenal team mate Thierry Henry, are struggling second from bottom of the Ligue 1 standings ahead of a crunch game against neighbours Olympique de Marseille on Sunday.
"I'm here to help the team and I'm impatient to start".
Fabregas puts pen to paper on a three-and-a-half-year deal at the Stade Louis II after passing a medical earlier in the day on the Mediterranean coast.
"Wow. I'm honored to announce that I will be starting an exciting journey with this wonderfully historic club".
Maurizio Sarri recently stressed that he would only be happy letting Fabregas leave Chelsea if he could sign an adequate replacement, highlighting the Spaniard as his only back-up for Jorginho in the deep-lying playmaker role.