The teenager enjoyed a breakthrough campaign last season, scoring five goals in all competitions and making his England debut, and he is widely regarded as one of the club's brightest young talents.
Hudson-Odoi is recovering from an Achilles injury but spoke about his delight at committing his future to the club, per Chelsea's official website.
"It's an amazing feeling," he 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."
Matt Law at the Daily Telegraph offered some detail on Hudson-Odoi's new salary:
The teenager is the latest Chelsea youngster to commit his future to the club, as Goal's Nizaar Kinsella noted:
Securing Hudson-Odoi's future will be a big boost to Chelsea. The teenager was linked with a move to Bayern Munich in the January transfer window and submitted a transfer request, per Dominic Fifield at the Observer.
The teenager had become frustrated by a lack of game time under then-manager Maurizio Sarri.
However, Chelsea managed to keep hold of him and he went on to impress when he was afforded first-team starts:
His performances also saw him called into Gareth Southgate's England squad, and he made history in their UEFA 2020 European Championship qualifier against Montenegro in March:
Hudson-Odoi's season was prematurely ended by an Achilles injury suffered in a 2-2 Premier League draw with Burnley.
He underwent surgery in April but has said he is now fit and ready to return:
The teenager can expect plenty of opportunities under new manager Lampard. The former midfielder told BBC Radio 5 Live (h/t Reuters) he has "no fear" in playing his youngsters if he feels they are ready.
Chelsea have demonstrated their faith in Hudson-Odoi by handing him a new contract, and Lampard's commitment to youth will encourage the teenager. His return from injury will be a welcome boost to the club after a tricky start to the season, and much will be expected from the talented youngster this season.