Alba still had one year remaining on his contract but will be seeking a new challenge after winning his sixth La Liga title with the Blaugrana.
The 34-year-old, a constant fixture at left back since signing from Valencia in 2012, has also won the UEFA Champions League and five Copa del Reys during his time at the Camp Nou.
Alba has made 458 appearances in total for Barcelona, scoring 19 goals and registering 91 assists.
Alba joins Sergio Busquets as another senior member of the Barcelona side who will be leaving this summer.
A club statement on Alba's departure reads: "FC Barcelona and Jordi Alba have reached an agreement to terminate the player's contract with the club one year earlier than it was due to expire at the end of the 2023/24 season.
"FC Barcelona would like to publicly express its gratitude to Alba for his professionalism, commitment and dedication, and his ever-positive and friendly relationship with all members of the Barça family, and wishes him every fortune in the future. Barça will always be a home for you, Jordi."