The 19-year-old has agreed a two-year deal with the Ligue 1 champions after spending three seasons at Stamford Bridge.
"I am really pleased and honoured to join Paris Saint-Germain," he told PSG's website. "Not only is this club a great reference in France and Europe, but it is also renowned for allowing many young players to express their potential in recent years.
"After my experience in England, I will do my best to continue my progress here with a fantastic squad and especially with top-level goalkeepers. I can't wait to join training next Monday."
Bulka enjoyed success with Chelsea Under-18s and played in the UEFA Youth League, although he did not make a senior appearance.
The Poland youth international suggested this year in an interview with TVP Sport that he had chosen to run down his Chelsea deal because promises had not been kept at the club.