The 24-year-old Belgium international becomes the fourth high-profile arrival at the Etihad Stadium after Raheem Sterling, Fabian Delph and Nicolas Otamendi.
De Bruyne said: “I want to reach the highest level possible as a player and I think the most important thing is that at the end of the season we can be happy and maybe have some titles.”
Pellegrini added: “It takes a special footballer to improve our squad and I have no doubt that Kevin is certainly one of those – he has all of the mental, physical, tactical and technical attributes required to fit straight in.
“We like to play attractive, attacking football and bringing in a player like De Bruyne will only aid us as we fight on four fronts.” De Bruyne joined Wolfsburg in January 2014 for a reported £16.7m after making three Premier League appearances for Chelsea.
He first arrived in the Premier League from his native club Genk in January 2012, with Chelsea reported to have paid a fee in the region of £6.7m for his services.
He scored twice in 13 appearances and 10 goals in 33 games in two separate loan spells at Genk and German club Werder Bremen respectively, during his two-year spell at Chelsea.
De Bruyne scored 10 goals in 34 league games for Wolsfburg last season, and his 112 chances created in all competitions was only second to Dimitri Payet’s tally for Marseille in European top-5 football last season.
The deal was already imminent at the weekend after Wolfsburg sporting director Klaus Allofs confirmed the Premie League leaders were ready to pay the Belgian hefty wages.
Allofs said after the confirmation: “We would have loved to carry on working with Kevin, but we decided to accommodate his wishes of moving to Manchester City now.
“He behaved in an absolutely professional manner during 18 months with Wolfsburg and he always gave everything.
“His transfer is regrettable because he was a key member of our team, but we are still well equipped to be able to continue along the successful path we have been on in recent months. We wish Kevin a lot of success with Manchester City.”