Chelsea have confirmed the deal on their official website.
The talented Belgian midfielder was linked with a move to Manchester United earlier this season.
Musonda was frustrated with the lack of first-team opportunities at Stamford Bridge and was ready to leave permanently after Chelsea failed to provide him with chances.
The Belgian signed a new deal at Stamford Bridge after promises of first team opportunities, but the Blues have failed to deliver on those promises.
Musonda is a highly talented attacking midfielder who is highly rated within the game. The Belgian is as talented as the likes of Hazard and De Bruyne and could develop into a world class player in future.