Financial details were not disclosed, but media reports said PSG paid €50 million ($57.83 million) for the 26-year-old.
"I'm delighted to be beginning a new adventure at such an ambitious club as Paris St Germain," Torres said in a statement.
"I'd like to thank President Nasser Al-Khelaifi, (PSG's football advisor) Luis Campos and coach Luis Enrique for giving me the opportunity to join the team, which I hope to help win as many trophies as possible."
Spain's World Cup hero arrives in the French capital after scoring an extra-time winning goal in the World Cup final against Argentina.
The forward scored 21 goals and provided three assists in 49 appearances across all competitions for Barca in their last campaign as the club retained their LaLiga title.
Torres joined Barcelona in 2022 after a brief spell at Premier League side Manchester City.
He has scored 25 goals in 65 appearances for Spain and will be reunited with Luis Enrique, having previously played under the Spaniard during his time in charge of the national team.