Fabregas is joining Monaco on a three-and-a-half year deal having joined the Blues from Barcelona in 2014.
Having previously made over 300 appearances for Arsenal, Fabregas moves to Ligue 1 with 501 outings in England.
He will team up with former Gunners team-mate Thierry Henry at Monaco, with the Frenchman in charge at the strugglers.
Chelsea posted a montage of many of Fabregas’s best moments in a Blues shirt with the Spaniard narrating.
“Since I was little I always preferred the feeling the assist gave me than the goal,” Fabregas said.
“Then when I grew up, I started scoring a little bit more goals and to be honest that does give you a great feeling.
“But I believe the main attribute in my career has been the final ball.
“It is always important to have an assist or be part of the play that gets you a goal.
“My type of football has always been to play with the ball, have the ball, create chances.
“As long as we are winning the confidence of the team will be higher and higher and then we can start being, it’s impossible to be perfect, but as close to perfection as possible.”
Fabregas could make his Monaco debut this weekend against Marseille.
(Fabregas thanked Chelsea and fans on Twitter)
And Chelsea announced the transfer with a classy statement.
It read: "Cesc Fabregas has today completed a permanent transfer to Monaco.
"The midfielder’s switch to the Ligue 1 club brings the curtain down on his four-and-a-half year Chelsea career, a period in which he won four major trophies, including two Premier League titles.
"The Spaniard made 198 appearances for Chelsea, scoring 22 goals.
"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."
Fabregas appeared to say his goodbye to Stamford Bridge last weekend as Chelsea beat Nottingham Forest in the FA Cup.
It wasn’t the perfect farewell though with the midfielder missing a penalty in the 2-0 win.