Choupo-Moting has joined Hansi Flick’s side on a one-year contract after his deal at Paris Saint Germain ended at the conclusion of the previous campaign.
The former Cameroon international makes a return to the Bundesliga after three seasons away, playing for Stoke City in England and turning out for the French champions in the last two seasons.
Choupo-Moting has previously represented the likes of Hamburg, Nurnberg, Mainz 05 and Schalke 04, and Bayern Munich will be his fifth German side.
The 31-year-old will serve as back-up to Robert Lewandowski in Bavaria. He appeared as a late substitute against his new employers in the Champions League final in August but could not prevent defeat for PSG.
"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.
"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."
