The clubs did not disclose financial details, but British media said the total deal was worth up to $224 million (£116 million), surpassing the package of up to $222 million (£115 million) that Real Madrid agreed to pay Borussia Dortmund for Jude Bellingham in 2023.
"Anderson, 23, is competing at the World Cup with England and has completed a medical in Kansas. The formalities of the move will be finalised upon his return to England," City said in a statement.
The move also makes Anderson Manchester City's most expensive transfer, eclipsing the $193 million (£100 million) they spent to buy winger Jack Grealish from Aston Villa in 2021.
Anderson, a product of Newcastle United's academy, joined Forest for $67 million (£35 million) in 2024 and made 92 appearances for them in all competitions, scoring six goals and providing 11 assists.
The midfielder has earned a reputation as a high-energy, tactically sound player, combining defensive solidity with the ability to contribute further up the pitch.
He is particularly known for his relentless work-rate, with strong pressing and ball recovery abilities as well as having a high rate of progressive passing and carrying the ball forward.
Hoffenheim's Ivory Coast winger Bazoumana Touré is set to join EPL side Newcastle United.
The 20-year-old is being linked with a $96 million (£50 million) move to north-east England, which would be a record transfer income for the Bundesliga side.
Newcastle need a new left winger after selling England's Anthony Gordon to Barcelona.
