Toure was a key player in the all-conquering Barca side of 2009 and, while the emergence of Sergio Busquets limited his opportunities last season, he is still considered among the best midfielders in the game.
Having made the move to City this summer, Kompany feels Barca's loss is City's gain and that Toure will make a major difference to their hopes of becoming an elite club in Europe.
"Toure is a natural-born winner and he will add so much to our team," he 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."
Toure joined City for a fee believed to be in the region of £24 million in July.