The 26-year-old England international made 235 appearances over eight seasons at Elland Road.
"I am absolutely delighted to have joined Manchester City. City have again proved to be the best team in the country," Phillips said.
City are understood to have agreed a £45m deal for Phillips, who had two years left on his Leeds deal.
He said City have "an amazing squad and a manager in Pep Guardiola who is rightly considered to be the finest in the world".
He added: "To be able to play under Pep and learn from him and his coaching staff as well as be part of such a fantastic squad is a prospect that I am incredibly excited about."
Phillips made his international debut in September 2020 and was named England men's Player of the Year for 2020-21, having played every game at the delayed Euro 2020 tournament.