The 36-year-old former Barcelona and Sevilla defender scored eight goals in 73 appearances for PSG after joining from Juventus in 2017, BBC Sport reported.
Alves scored in Brazil's 5-0 victory over Peru in their final Copa America group game on Saturday.
"Today I close another cycle in my life, a cycle of victory, learning and experiences," he said on Instagram.
"It was two years of resilience and continuous reinventing to fulfil my mission, but in life everything has a beginning, a middle and an end and now the time has come to put that final point here.
"I apologize if at any point I was not up to the pitch, I apologize if at some point I made a mistake, just tried to give my best."
During his spell at Parc des Princes, Alves won back-to-back Ligue 1 titles, one Coupe de France and one Coupe de la Ligue.
Prior to joining Juventus, who released him after one season, Alves won La Liga six times as well as three Champions League titles with Barcelona.
"Thanks to all the companions for the moments lived, the laughter together, the boredom that your lazy spirits have put me through," Alves added.
"If you ever remember me, be like the good crazy of each day, with a beautiful smile on your face, with a pure energy of soul, as a professional worker and committed to the goals, as someone who just wanted you to be better each day and who tried to make them understand the true meaning of the word team.
"A big hug to all and hope you do not miss my crazy things."