The flamboyant full back joined the French club in 2017 after spells at Sevilla, Barcelona and Juventus, but he did not say what his next move would be after leaving Paris.
The club later added that both parties had agreed not to extend Alves' contract.
"Another cycle in my life ends today, a victorious cycle, one of learning and experiences," Alves, 36, wrote on Instagram.
"I would like to thank the PSG family for the opportunity we had together to build a page in the club’s history."
Alves, who replaced club mate Neymar as Brazil captain for the Copa America last month, won two Ligue 1 titles and one French Cup in his two seasons at Parc des Princes.
PSG chairman Nasser Al-Khelaifi hailed Alves, who scored eight goals and made 18 assists in his time in Paris, for "the professionalism and experience" he brought.
"We are happy to have had a player of the talent and experience of Dani Alves here at PSG for two seasons. Two years ago, following his experiences in Spain and Italy, Dani chose PSG when he wanted a new challenge," Al-Khelaifi added.
"We are happy that this great player leaves Paris having won several trophies in our colours. I wish him the best in the challenges that lie ahead of him."
(Reporting by Andrew Downie; additional reporting by Shrivathsa Sridhar in Bengaluru, editing by Nick Mulvenney and Christian Radnedge)
