After returning to the Camp Nou, the 110 times-capped former Spanish global won one La Liga title, one Copa del Rey, and one Fifa Club World Cup.
Fabregas described the move as "a new project", calling it a "great honour".
Fabregas left the pitch in tears after making his final appearance for Chelsea in last Saturday's FA Cup third round win over Nottingham Forest.
"There is no doubt Fabregas's place in the Chelsea history books is assured given his achievements over the past four-and-a-half seasons", a club statement read.
Key to the move was the fact that Monaco are now coached by Fabregas' former Gunners teammate Henry, with whom he won the Premier League in 2004. "I'm here to help the team and I'm impatient to start".
Avoiding serious injury helped him to play around 650 club games and to score 121 goals - winning league titles with Barcelona and Chelsea and domestic Cup competitions with all three sides. "I am very excited".
However, Maurizio Sarri's arrival ahead of 2018-2019 effectively spelled the end of Fabregas's Chelsea career, as the Italian brought in his former Napoli midfielder Jorginho, who instantly took the Spaniard's position.
Vice-president Vadim Vasilyev added: "We are very pleased to welcome to AS Monaco Cesc Fabregas, a world-class player and a great professional, whose arrival demonstrates the ambition of the club".
"We are convinced that his experience at the highest level will bring a lot to our players on and off the field".