Sibierski has signed a three-year contract with City after the club finally reached an agreement with Lens to secure the playmaker's services.
City have splashed out in the region of £750,000 to land the 29-year-old and beat off competition from La Liga to snare the schemer.
Both Atletico and Soceidad are believed to have contacted Sibierski but Lens chairman Gervais Martel revealed the Frenchman wanted a switch to The Premiership.
Martel also lamented Sibierski's decision to leave Lens but conceded he could not stand in the player's way.
"It is a shame to see him leave," opined Martel. "I never retain a player against his will.
"We didn't really have the means to compete with Manchester City and I quickly understood Antoine dreamt of discovering The Premier League."
Lens are now stepping up their search for a replacement and the early candidate to fill Sibierski's shoes is Camel Meriem.
The Bordeaux attacking midfielder has emerged as a prime candidate for Lens and may be amenable to leaving Parc Lescure.
