Hudson-Odoi has struggled for game time at Stamford Bridge since the arrival of Thomas Tuchel as manager in January 2021, and is yet to feature at all this season.
The 21 year-old has played 126 times for Chelsea in all competitions since making his debut in 2018, with 37 goal involvements (16 goals, 21 assists).
The Premier League club confirmed it has the option to recall the player in January.
Several clubs in England and Germany were credited in the media with an interest in Hudson-Odoi, but the winger has opted to join Gerardo Seoane's team for the campaign.
Speaking to the club's website after the move was confirmed, Hudson-Odoi said: "The move to Germany is really exciting for me and I can play in the Champions League with Bayer 04 Leverkusen.
"That combination is really attractive and I'm keen to get to know the club, the fans and the Bundesliga. [Chelsea team-mate] Kai Havertz only had good things to say about it to me."
Leverkusen secured their first victory of the Bundesliga season on Saturday as they won 3-0 at Mainz, having lost their first three games.
Three-cap England international Hudson-Odoi – who was close to joining Bayern Munich in 2019 – could make his debut on Sunday (AEST) when Freiburg visits the BayArena.