The defender says stars such as Sergio Aguero and Wilfired Bony will help the former Liverpool star to flourish.
The Blues completed their big money move for the England man earlier this week after months of speculation about his future at Anfield and a possible move to the Etihad.
And he believes the capture of the youngster is an important one as their Premier League rivals are all adding this summer, with Arsenal, Manchester United and Chelsea already having brought in new faces.
“We have great quality in the team but you can’t compete nowadays if you don’t improve every year,” he told MCFC.com.
“Other teams improve, we need to improve and getting him puts us one step closer to being this team which can win trophies again – it’s very important for us.”
City stars will make Sterling better
The defender also believes that the players at Manchester City will only help to make Sterling a better player.
The youngster arguably enjoyed his best season to date when he was playing alongside Luis Suarez the season before last, as the Uruguayan pushed the Reds in a hard fought Premier League title challenge.
Suarez was arguably the star of the show at Anfield in that season, and Kompany believes Sterling playing with the likes of Sergio Aguero and Wilfried Bony will only benefit the 20-year-old.
“He was one of the main reasons, along with Suarez, that Liverpool played so well,” added Kompany.
“What you will find is that he will have this kind of structure at City already. We’ve got Kun up front, we’ve got Bony, we’ve got so many players who will be able to link up with him we will be able to make him better as well.”