[4] On 11 June 2012, Musonda joined Chelsea, along with his two older brothers,[5] after the club previously agreed to pay a "compensation fee" to Anderlecht.

[12] On 29 January 2016, Musonda joined La Liga side Real Betis on loan until the end of the season, without the option of making the move permanent.

[17] With manager Antonio Conte unsure whether Musonda was to stay with the Blues or be loaned out, interest arose from many clubs around Europe, including Roma.

[18] However, after the conclusion of the January transfer window, Antonio Conte confirmed in a post-match press conference preceding Chelsea's 1–1 away draw with Liverpool, that Nathan Aké, Kenedy and Musonda would be staying at the club for the rest of the 2016–17 campaign.

[20] He made his first starting appearance for the club in an EFL Cup tie against Nottingham Forest, scoring the third goal in a 5–1 victory on 20 September 2017.

[23] In February, he provided the assist for Callum McGregor's goal in a 1–0 win over Zenit St Petersburg in the first leg of the round of 32 stage of the Europa League.

[27] One week into his initial loan period, Musonda suffered a posterior cruciate ligament injury, which restricted him to just four league appearances over the next two seasons.

[28][29] However, the Belgian still decided to go through recovery and work on regaining his fitness and condition, eventually returning to team training between December 2020 and January 2021.

[29] Musonda was subsequently aggregated to the Blues' Under-23 squad: on 24 September 2021, he started and played for 61 minutes in the Premier League 2 match against Liverpool, which ended in 4-3 win for his side.