After year-long negotiations, the 18-year-old winger has signed a £150k-per-week, but with performance add-ons could end up totalling £180k-per-week.
"It's an amazing feeling,' Hudson-Odoi said. "It's been a long wait but it's done now and I'm really happy about that. I've been a Chelsea player since I was eight and this is the right club for me to be at.
"I want to lift as many trophies as possible, win as many games as possible and contribute to as many goals as I can as well.
"As a team, we just want to work hard to achieve the best results we can. I'm delighted everything has been agreed and now I'm just looking forward to properly getting back."
Hudson-Odoi handed in a transfer request in January and was the subject of four rejected bids from Bayern Munich.