The departures of Puyol and goalkeeper Victor Valdes - second deputy - at the end of last term left two vacancies in the Camp Nou leadership ranks.
However, they have now been filled following a vote among the club's players.
Xavi, who announced his decision to stay with the Catalan giants this week, steps up from the vice-captain position he held for six seasons, while Andres Iniesta will serve as back-up to his midfield colleague.
The two newcomers to the foursome are Lionel Messi and Sergio Busquets, who has also inherited Puyol's famous number five shirt.
Both Messi and Busquets have previously worn the captain's armband when more senior players have been unavailable.
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