That price is a huge drop from the summer of 2020, when Bayern Munich offered to take Hudson-Odoi on a season-long loan with a £70m obligation to buy.
Chelsea ended up rejecting that bid and kept him at Stamford Bridge but it has not worked out for the 22-year-old versatile attacker since then.
The Blues sent him out on loan to German club Bayer Leverkusen last term, where he also struggled, and Chelsea have now decided to offload him permanently.
Hudson-Odoi, who came through Chelsea’s academy, registered 16 goals and 22 assists across 126 games for the west Londoners and has paid tribute to the club’s fans.
‘To the Blue Army… The time has come for me to bid Chelsea FC farewell,’ Hudson-Odoi posted on social media with a video highlighting his favourite moments with the Blues.
‘For the longest time, Chelsea has been my home. My best memories will always be playing in front of you all at The Bridge.
‘I would like to thank everyone that has supported me so far. Until next time. CHO.’
Hudson-Odoi, speaking to the Forest website after his move to the City Ground was confirmed, added: ‘It’s massive for me to be here and I can’t wait to get started. 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.’