After returning to the Camp Nou, the 110 times-capped former Spanish worldwide won one La Liga title, one Copa del Rey, and one Fifa Club World Cup.
The midfielder has finally completed his move to the Ligue 1 strugglers on a three-and-a-half year deal.
The source told AFP that Chelsea will only receive payments related to Fabregas' performance on the Mediterranean coast, contrasting with media reports that Monaco had already agreed to pay Chelsea 10 million euros ($11.5 million) for the player who could now make his debut for his new club in Sunday's Ligue 1 game away at Marseille.
"It is a great pleasure to join AS Monaco, a new project for me", Fabregas said in a statement.
During 501 appearances in English football, he won two Premier League titles, two FA Cups and a League Cup. "It is a quality squad with young players and a young coach", said Fabregas, referring Henry.
The 31-year-old Fabregas struggled to earn regular first-team action with the Blues this season and had made just six appearances in the Premier League this season prior to his departure.
"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".
The Premier League club are understood to be interested in deals for Cagliari midfielder Nicolo Barella and Zenit St Petersburg midfielder Leandro Paredes.
"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".