Hudson-Odoi, who has two caps for the Three Lions of England, will earn in excess £100,000 a week and brings to an end months of speculation surrounding his future at Stamford Bridge.
Hudson-Odoi, who was the subject of a failed bid of £35m from German champions Bayern Munich in the January transfer window, played 23 times in all competitions for Chelsea last season and scored five goals.
The Chelsea academy graduate handed in a transfer request when Bayern came calling but has now had a change of heart with Frank Lampard instrumental in keeping him at the club.
"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."
The 18-year-old saw his season curtailed by an Achilles injury suffered against Burnley in the Premier League in April and has recently resumed full training.
"I have seen Callum come through and he's a fantastic talent," manager Frank Lampard added.
"He is going to be central for us on the pitch and that is the opportunity in front of him now.
"There are things as a young player that he will want to improve but he can be central to this team and for England. I want to work with him, I want to drive him forward and I want to improve him as a player.
"Callum can show, right here at Chelsea, the club he came through the academy at, that he is going to be a world-class player because I truly believe that."