The former Barcelona and Juventus defender revealed the news in an Instagram post, in which he explained that he was closing another chapter of his career.
"Today I close another cycle in my life, a cycle of victory, learning and experiences," Alves wrote in a lengthy statement.
"I would like to thank the PSG family for the opportunity to together build a page in the history of this club.
"I would like to thank all the staff for their affection, respect and complicity from day one ... you make this club a little more special."
The 36-year-old joined PSG from Juventus in 2017 and has won two Ligue 1 titles in that time, though the team have failed in their Qatari owners' stated aim of winning the Champions League.