Fabregas waved goodbye to the Blues supporters after their FA Cup victory over Nottingham Forest a week ago, which proved to be his final game.
The Spaniard has now completed the move to Monaco, signing a three-and-a-half year deal.
"We are very pleased to welcome Cesc Fabregas to AS Monaco, a world-class player and a great professional, whose arrival demonstrates the ambition of the club," club vice-president Vadim Vasilyev said in a statement.
"We are convinced that his experience at the highest level will bring a lot to our players on and off the field."
Fabregas will wear the number 44 jersey during his time with the former Ligue 1 champions.