The 23-year-old began his career at Newcastle United before joining Forest in 2024, quickly becoming a key figure at the City Ground and missing just one Premier League game across his two seasons there.
A box-to-box midfielder known for his energy, tackling and creative passing, Anderson arrives at the Etihad with 174 senior appearances and seven England caps behind him, having cemented his place in Thomas Tuchel's plans over the past year.
"City are one of the biggest clubs in the world and the squad they have is amazing - so strong in every position," Anderson said after signing.
"As soon as I knew they wanted me, I was absolutely determined to make this move happen. As a footballer, you want to test yourself at the highest level.
"Being at City means I have that opportunity. It's a club built to win trophies and compete at the very top of the game. That is exciting for any footballer."
Director of football Hugo Viana praised the qualities that convinced Manchester City to move for the midfielder.
"Elliot is one of the outstanding young midfield talents in world football right now. He offers energy, outstanding work rate and an exceptional range of passing. His improvement in recent years has been really impressive. At just 23, there is plenty of opportunity for development over the coming years and we feel he can become a complete midfielder."
Anderson also spoke about his excitement at working under Maresca, who joined City this summer after leading Leicester to the Championship title and Chelsea to Conference League and Club World Cup success.
"I've watched his teams over the past couple of years and spoke to a few of the lads from Chelsea and they all rate him very highly," Anderson said.
Asked whether his own playing style would suit the Italian's approach, he added: "I like to be intense when I play and use lots of energy around the pitch and get the fans going, so I think that'll be good."
Former Forest boss Ange Postecoglou, who coached Anderson at the City Ground, has previously described the midfielder as a natural fit for a Maresca side.
The move comes on the back of a memorable World Cup for Anderson, who played a part in England's run to the semi-finals before Thomas Tuchel's side were eliminated by Argentina.
"It was disappointing, but I loved it personally," he reflected. "As a team I think we had the whole country behind us and we've done so well but just fell short. From a personal point of view, I enjoyed it and I thought I'd done pretty well."
He said he now planned to take around three weeks off before reporting for pre-season training.
Anderson was candid about the scale of his own ambition, insisting there remains plenty of room for improvement despite his rapid rise.
"I'm only twenty-three, so I've got plenty of time to get to my best levels. I definitely think I'm not there yet and there's more to come from me. I think I bring a bit of everything - quality, physicality, energy. I'd like to think I'd get the fans excited and bring energy to the team. I love having the ball at my feet, and I'll help the team out when we're in tough times."