La Blaugrana struck a big-money deal for Torres with Manchester City earlier this winter but could not register the attacker due to their long-running financial problems.
Barca's economic issues were alleviated following Philippe Coutinho's loan move to Aston Villa, and Umtiti's recent extension means that Torres can now take part in La Liga matches due to the club's FFP quota increasing.
A statement on fcbarcelona.com read: "FC Barcelona and first team player Samuel Umtiti have reached an agreement to extend the latter's contract until 30 June 2026. The French defender is reducing a part of the salary that he was due to receive in the year and a half remaining on his contract.
"This contract extension operation does not entail any greater financial commitments for FC Barcelona with regard to the player.
"FC Barcelona wishes to publicly express its gratitude to Samuel Umtiti for his willingness and the affection that he has demonstrated towards the club. Through this contract extension, FC Barcelona will be able to increase its 'financial fair play' quota and thus register Ferran Torres with the Spanish Professional Football League."