The former Spain midfielder was Puyol's deputy last term and won a vote of his teammates to take on the armband on a permanent basis after deciding to remain at Camp Nou.
The 34-year-old will be assisted by Andres Iniesta, who will be his immediate deputy, ahead of Lionel Messi and Sergio Busquets.
Last term, Victor Valdes was the third captain after Puyol and Xavi, but the goalkeeper left the club this summer after his contract expired. The Spaniard is currently recovering from an anterior cruciate ligament injury and is without a club.
Xavi has spent his entire career at Barcelona, making close to 500 Liga appearances for the Catalan giants since making his debut in 1998.
He has won a stunning seven Primera Division titles in his time at Camp Nou, along with three Champions Leagues and two Copa del Reys.
This week, he announced his retirement from the international scene and revealed that he was close to leaving the club this summer, but was persuaded to stay by new coach Luis Enrique.