City are set to pay an initial £42 million to sign the midfielder with another £3m due in add-ons. Midfielder Darko Gyabi, 18, will join Leeds in a separate deal worth £5m.
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Phillips will next finalise personal terms with City before undergoing a medical. The 26-year-old should complete his move to the Etihad Stadium in time to join up with Pep Guardiola's squad for their tour of the United States.
He will compete for a place in midfield with Rodri and replace Fernandinho in the squad after the Brazilian departed at the end of last season following nine years at the Etihad. Sources have told ESPN that City's summer spending could yet increase if they can agree a fee with Brighton for Spanish left-back Marc Cucurella.
Phillips, who was also linked with a move to Manchester United, has spent the last two seasons in the Premier League after Leeds' promotion from the Championship in 2020.
He made his international debut for England the same year and played a key role in their run to the final of Euro 2020 where Gareth Southgate's side were beaten on penalties by Italy. He leaves Leeds having made 234 appearances for his boyhood club, scoring 14 goals.