Hudson-Odoi has fallen down the pecking order at Stamford Bridge under manager Thomas Tuchel and was an unused substitute in each of their Premier League games this season.
Chelsea said they retain the right to recall the 21-year-old in January.
Hudson-Odoi has suffered from lengthy injury problems since making his senior Chelsea debut in 2018, most notably an Achilles' tendon injury that sidelined him for five months.
He has not featured for Chelsea since an FA Cup win over Luton Town at the start of March.
"The move to Germany is really exciting for me and I can play in the Champions League with Bayer Leverkusen," Hudson-Odoi, who has made more than 100 appearances for Chelsea, said.
"That combination is really attractive and I'm keen to get to know the club, the fans and the Bundesliga."
On the club website, Bayer Leverkusen's sporting managing director Simon Rolfes described Hudson-Odoi as a "fast and penetrative winger."
"He has everything to be able to help us immediately," he said. "This will give our attacking game another special component. We're very happy this transfer has gone through."