The England international joins fellow academy products Ruben Loftus-Cheek and Mason Mount in committing to long-term deals since Frank Lampard's appointment as head coach.
Securing the teenager's signature is significant for Chelsea, who rejected several bids from Bundesliga champions Bayern Munich earlier this year.
The German giants made their interest known in January, reportedly leading Hudson-Odoi to submit a transfer request, and are said to have returned with a reduced £22.5million (€25.4m) offer as the winger entered the final 12 months of his previous deal.
Chelsea resisted Bayern's interest and have now tied the talented homegrown prospect to an agreement reportedly worth upwards of £100,000 per week.
"It's an amazing feeling," Hudson-Odoi told Chelsea's official website. "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."