The England international has agreed terms at the Etihad Stadium until the summer of 2028 and leaves Leeds after spending 12 years in the ranks at Elland Road.
Browsing: Kalvin Phillips
Leeds is chasing a number of reinforcements this summer with Raphinha and Kalvin Phillips set to leave Elland Road. Raphinha is closing in on a move to Chelsea, while Man City is close to wrapping up a deal for Phillips.
The visitors, who had lost four of their previous five league matches, were 3-0 up at half-time after goals from Matt Doherty, new recruit Dejan Kulusevski and Harry Kane.
Sterling broke through the middle of the Croatian defence and ran onto the end of a pass from Kalvin Phillips to fire home his 57th minute marker and get England off to a winning start in Group D.
The French forward followed up his four-goal haul in Sevilla in midweek by marking his first league start of the campaign with a brilliant first-time finish on 27 minutes.