"Long live Barca, long live Catalunya, long live the mothers who gave birth to you all," he said.
Alves played for Barca from 2008-16, winning six LaLiga titles, three Champions League crowns and three Club World Cups among other major honours.
But the club had to sell their biggest star Lionel Messi before the season because of financial difficulties, and sit ninth in the league.
Alves will wear the number eight jersey in his second stint, and said he wanted to pay tribute to two club greats who had the same number, Andres Iniesta and Hristo Stoichkov.
Alves, who completed his medical this week, cannot play until January but will start training with his team mates this week.
Despite playing a different role for Sao Paulo and the Brazil national team lately, Alves said he expected to play for Barca in his original position, right-back.
"I want to be able to bring a bit of joy, of hope to the team. I think that in recent times, the team has been burdened with negative things. It is time for that to change," he told reporters.