The England forward ended prolonged speculation over his future by leaving Liverpool for Premier League rival City earlier this month.
Sterling has already shown promise during preseason, scoring three minutes into his debut against Roma last week and also netting a brace in Monday's 8-1 thrashing of Vietnam.
While the fee paid to land Sterling has raised a few eyebrows, Pellegrini is confident the 20-year-old has the talent to justify his price tag.
"He is a very good player, that's why we brought him to our team," said the City manager. "He has a lot of things we didn't have in our squad. If you watch the way he played [against Vietnam] he has a lot of pace and I am sure in the future he will demonstrate why we paid so much money for him."
On the Vietnam result, Pellegrini added: "I was very surprised because it is not easy to score eight goals, but Vietnam is a team that must prepare for qualification for the next World Cup, and they have time.
"They start playing in September or October so have to work hard, but they have very good players."