The 21-year-old moves on from Old Trafford, with Forest believed to have paid United a fee of £15m.
Elanga had been with United since he was 12 and achieved a first-team breakthrough in 2021, making 55 appearances for the club in all.
“It’s a pleasure to be here. It’s a proud moment, not only for me, but for my family as well,” said Elanga.
“It’s a big step and I’m really looking forward to playing in front of the Forest fans at the City Ground.
“I had interest from elsewhere, but for me, Nottingham Forest feels like the perfect place.
“I’ve been here with United. It’s a special place, but being here with Forest, I feel like it will be even more special. I’m ready for the challenge.”
YOU CAN ALSO READ:2023 WWC Update: New Zealand Upset By World Cup Debutants
Elanga had been on United’s pre-season tour of the USA but travelled back to complete the move.
He is Forest’s first summer signing and joins Steve Cooper’s side despite interest from clubs in Germany and Everton, whom Elanga was close to joining on loan in January.
Elanga registered four senior goals for United and although he failed to score from 26 games last season, he made just seven starts.
Chelsea have rejected a bid from West Ham for England midfielder Conor Gallagher worth a reported £40m.
Gallagher, 23, has two years left on his contract and is currently on the club’s pre-season tour of the USA.
The Chelsea academy graduate enjoyed a successful loan spell at Crystal Palace in 2021-22, winning player of the season and making his England debut.
He made his Chelsea debut last season and went on to score three goals in 45 appearances.
Chelsea’s ownership group has been trying to avoid letting players enter the last two years of their contracts, a situation that played out with Mason Mount’s £55m move to Manchester United.
Chelsea like Gallagher but accept there is a chance he could leave.
Written by: Debby Eselebor