The Czech Republic international midfielder, who spent the whole of last season on loan at St Andrew's from Chelsea, has signed a three year deal with Gordon Strachan's side.
"I am very excited about joining Celtic and hope to play a part in bringing even more success to the club," he said of the move north-of-the-border.
Jarosik, who finished the season as joint top scorer with eight goals, would have signed a permanent deal with Blues had they not been relegation from the Premiership last season.