"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."
News of his new deal brings an end to months of speculation over his future.
Reports earlier this year suggested the 18-year-old was eager to leave Stamford Bridge due to a lack of playing time under former Chelsea manager Maurizio Sarri.
But Hudson-Odoi was ready to commit to the club once Sarri left and new manager Frank Lampard assured him he has a future at the club, Magowan adds.
"I have seen Callum come through and he’s a fantastic talent," Lampard said. "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."
Now that Hudson-Odoi's contract is complete, the Blues can shift their attention to signing other youngsters to new deals. Chelsea are reportedly in talks to sign forward Tammy Abraham and center-back Fikayo Tomori to long-term contracts.