Despite recently signing a new contract with Chelsea that lasts until 2022, the 21-year-old had long lined up for a loan move and had attracted interest from the likes of Real Betis, Bournemouth, Newcastle United, Watford and West Bromwich Albion.
However, it is the Scottish champions who have won the battle, landing his services until the end of the 2018-19 campaign after he went through a medical in Glasgow on Monday.
The Belgium Under 21 international will unite with Brendan Rodgers's side as they sit 11 points clear of Rangers at the top of Scottish Premiership and prepare for a Europa League last-32 tie with Zenit St Petersburg.
Musonda has featured for Chelsea's first team seven times in all competitions this season, most recently making a late cameo in the Premier League clash with Brighton and Hove Albion on January 20.
The Belgian previously spent time on loan with Real Betis in La Liga, where he made 14 starts and 10 further substitute appearances before an injury forced him to make an early return to Stamford Bridge in December 2016.
Musonda is not the only Chelsea player on the move Monday. Antonio Conte's side also saw Baba Rahman return to Schalke on an 18-month loan deal, while Brazilian attacking midfielder Nathan will head to Belenenses.
Meanwhile, the Premier League champions are set to secure their second signing of the transfer window, as Emerson Palmieri will travel to London on Tuesday to complete a £17.5 million move from Roma.