Goal reported last week that the 17-year-old centre-back was ready to trade the Premier League club for the Ligue 1 giants, who have earned a reputation for developing exciting young talent in recent years.
As a result of the move Chelsea are due a fee for the player, believed to be in the region of £2.5 million.
Panzo, who won the Under-17 World Cup with England in 2017, is delighted to have made the switch to the Ligue 1 club.
“It’s another step in my career. I’m motivated by the idea of working with the staff and playing alongside great players.
“I hope to be integrated as quickly as possible to help the club attain its objectives.”
Meanwhile, Monaco vice president Vadim Vasilyev sees the youngster as another valuable addition to the club’s project.
“We’re delighted to welcome him to Monaco,” he added. “He’s a player for the future who has already distinguished himself with the national team and with the Chelsea youth teams.
“We believe in him and his capacity to shine here at Monaco.”
One of the chief reasons that Panzo has been persuaded to move to the principality side has been the influence of sporting director Michael Emenalo, who was previously at Chelsea.
Monaco have also been linked with a move for Callum Hudson-Odoi, who broke into the Blues’ side under Antoino Conte, though they face competition from several big European clubs, including the likes of Barcelona, Real Madrid and Bayern Munich.
The French side have made several high-profile young signings so far this summer, including highly-rated Willem Geubbels, who arrived from Lyon for a fee of around £18m (€20m/$23m).
Additionally, Monaco have also moved to sign France Under-21 international Samuel Grandsir from Troyes, while Rennes youngsters Wilson Isidor and Sofaine Diop have also joined the Stade Louis II club.
In January, meanwhile, they completed the transfer of promising Italian teenager Pietro Pellegri, though his progress has been stalled by injury.