Brendan Rodgers has been a long-term admirer of Musonda and he has promised that he will help develop the young midfielder at Celtic Park.
Chelsea had a strong say in the player's temporary move, encouraging him to join a club where he is likely to get maximum game time.
Musonda is highly regarded at Stamford Bridge and signed a new deal until 2022 in January ahead of being told that he could leave the club on loan.
The youngster has previously spent time on loan with Real Betis in La Liga, where he made 14 starts and 10 further substitute appearances for the Liga side.
Michy Batshuayi, meanwhile, is another who could leave Chelsea on a temporary deal in the January transfer window.
The Belgian, who is wanted by Sevilla, says that his future is down to Antonio Conte. He told BT Sport after scoring twice in the 3-0 win over Newcastle: "I don't know [whether he'll leave in January].
"It's up to the boss, it's better to talk to Conte. It's [the win over Newcastle] very good for the team and for me I'm very happy.
"When I have a chance I take the chance and I work every day – I'm very happy."