The winger, 22, departs Chelsea after 15 years on the books at Stamford Bridge, where he scored 16 goals in 126 games.
Hudson-Odoi has signed a three-year contract at the City Ground with Forest accepting a sell-on clause as part of their tenth major addition of the summer.
“It’s massive for me to be here and I can’t wait to get started,” said the player after being given the No14 shirt.
“It’s a new chapter for me. I know a couple of the boys already which was a big thing for me, and I obviously know the manager well, so it’s nice to be here and see familiar faces around.
“Forest are a big club which won two massive trophies in its history and I’m really excited to play at The City Ground. I know all about the atmosphere having watched a couple of times and I can’t wait to get playing in front of the Forest fans.”
Hudson-Odoi worked with Steve Cooper in the England youth set-up, as part of the victorious Under-17 World Cup winning side in 2017.
Fulham were also keen on the former Bayer Leverkusen loanee and launched a late bid to snatch him from under Forest’s noses, but are instead set to land Everton’s Alex Iwobi for £20m.