The 31-year-old made 51 appearances across all competitions for PSG following his surprise move from Stoke City, scoring nine goals.
Choupo-Moting, who has previously played in the Bundesliga for Hamburg, Nurnberg, Mainz and Schalke, has signed a one-year deal with Hansi Flick's side.
"It's a great feeling to come back to the Bundesliga and then to the biggest club in Germany," he told the club's official website.
"It’s an honour to play for this club. It’s always #FCBayern’s aspiration to win everything, and I’m hugely motivated to help them achieve those goals." 🔴⚪#ServusChoupo 👋 #MiaSanMia pic.twitter.com/U26AhmMo9Q— FC Bayern English (@FCBayernEN) October 5, 2020
"Who wouldn't want to play for Bayern? It's an honour to play for this club. At Bayern, the aim is always to win everything and I am highly motivated to achieve these goals."
Sporting director Hasan Salihamidzic added: "I am happy that we were able to sign Eric. He gives our squad a depth on the offensive, especially in the centre, which we will need.
"Eric gained international experience at Paris Saint-Germain, he knows the Bundesliga, and he is coming on a free transfer. It all fits together very well."
Choupo-Moting arrives at the Allianz Arena a day after Marc Roca joined the club from Espanyol for a reported €15million.