The France under-18 international is a product of the PSG academy, which he joined at 14.
The 18-year-old made his professional debut during the 2019/20 season and had 13 appearances for PSG, including two in the Champions League, before the French league season was halted in early March due to the coronavirus pandemic.
"In our eyes, he is one of the biggest talents in Europe," said Bayern's sports director Hasan Salihamidzic.
"His main position is centre-back, but he can play in other positions. We are sure he will have a big career and will strengthen our squad."
Bayern dominance
Bayern wrapped up their eighth consecutive Bundesliga title at Werder Bremen on 16 June. They were presented with a record-extending 30th top flight title on 27 June after a 4-0 waltz past Wolfsburg.
There could be further celebrations. On 4 July, Bayern face Bayer Leverkusen in the German Cup final in Berlin.
Success in the showdown would furnish them with their second consecutive league and cup double and 14th overall.
They could also add the Champions League crown to a bulging trophy room. They are in the last eight of the tournament which has been reconfigured due to the coronavirus pandemic.
"I am very happy to be able to play for such a large and traditional club," said Kouassi. "I could hardly wait to sign the contract.
"I really hope that I will do well here and I'll work hard to make that happen."
Kouassi is the second signing Bayern have made for next season on a free transfer. Schalke goalkeeper Alexander Nuebel has also been drafted in. The 23-year-old is expected to rival and eventually succeed club captain Manuel Neuer.
According to British and German media reports, Bayern are on the verge of wooing the Germany international Leroy Sane from Manchester City.
