Toure, who had played a key role for the Catalan giants in recent years, was permitted by Barca coach Pep Guardiola to depart the Nou Camp this summer in a £28million move to Eastlands.
But new City team-mate Kompany has tipped Ivory Coast star Toure to make a big impact in Manchester, and believes the Spanish club could end up regretting their decision to let the Ivory Coast star go.
"Toure is a natural-born winner and he will add so much to our team," defender Kompany told the Daily Star.
"I cannot understand why Barcelona let him leave. He has a big challenge to help us become one of the best teams in the Premier League and Europe.
"He is so important because of the great experience that he has and gives us something which we have lacked in the team."