Monaco have scored just 16 goals in the league this season, and a reliable striker would help fire them out of the relegation zone.
Given Monaco's precarious position, and his ability and experience, Fabregas could go straight into the side.
And on the £10m switch, new No.44 Fabregas told Monaco's official website: "It is a great pleasure to join AS Monaco, a new project for me".
"I'm looking forward to starting, we have a great match to play in Marseille on Sunday".
Now 31, Fabregas eventually made the same move as Henry when he left the Emirates Stadium for Barcelona, but he returned to English football with Chelsea in 2014. "I am very excited".More news: Spider-Man on PS4 is getting something 'fantastic'
The 2010 World Cup victor has penned a three-year deal with Monaco, who has been struggling in the French top flight this season.
However, he could not establish himself the same way under Maurizio Sarri and he managed just one Premier League start for the club prior to his confirmed departure.
Having enjoyed a glittering career, capped by winning the World Cup with Spain in 2010, Fabregas arrives at a club who were French champions just 18 months ago but are now in crisis.
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.
Henry has signed two defenders so far during the transfer window: 22-year-old Fode Ballo-Toure from Lille and 36-year-old Brazilian Naldo from Schalke.
Fabregas will move to Monaco without a fee for now, as Chelsea will be paid via bonuses depending on the Fabregas's performances.