While more signings are expected to arrive at the Etihad Stadium, Kompany is pleased with the way Rodwell is settling into the team.
"Jack has settled in really well," said Kompany.
"His performance was ahead of what you would have expected from someone who just came in for his first game after two training sessions. Maybe it was the right moment to introduce him. In any event, it paid off.
"Now the tough games come and I am sure we will gain a lot from having him with us."
City take on Liverpool at Anfield in their second Premier League game of the season on Sunday.