Torres etched his name into the history books by scoring the only goal of the final in extra-time as Spain defeated Argentina.
The forward was a prime target for PSG, despite their other signings in this position which includes Maghnes Akliouche.
Torres will wear the No 9 shirt in Paris and has signed a deal until 2031.
In 207 matches for FC Barcelona, Torres netted 65 times, including in the Copa del Rey final victory against Real Madrid - one of six major honours he won in Spain.
The transfer potentially frees up some funds for Barcelona's pursuit of Manchester City midfielder Rodri.
City rejected a £55m bid from Barcelona for Rodri last week but the Catalan giants remain determined to sign him and are considering their next move as talks remain ongoing.
