After starting out with Arsenal as a roaming attacking midfielder with a clinical eye for goal and a deft pass, Fabregas moved into a deeper-lying position over the years where his vision of the game and outstanding passing range helped him to remain influential in games with Chelsea.
"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", said club vice-president Vadim Vasilyev.
After winning two Premier League titles with the Blues, he has fallen out of favour at Stamford Bridge this season under new coach Maurizio Sarri.
What his departure does do is free up a large chunk of Chelsea's wage bill, with Fabregas the third-highest paid player at the club behind N'Golo Kante and Eden Hazard despite only having six months left on his contract.
Fabregas arrived at Stamford Bridge as a 2012 European Championship and 2010 World Cup victor with Spain.
The former Marseille and Roma player was expected to put pen to paper on a move from Turkish club Antalyaspor, but Monaco announced earlier on Friday that he had failed a medical due to a calf problem.
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