Bayern let their option to buy Perisic expire, but held a new round of talks with Inter in recent weeks.
The Bavarians reportedly offered €12m to sign Perisic, but it does not appear to have been successful.
In an official statement, Bayern said farewell to the Croatian international.
Bayern sporting director Hasan Salihamidzic was full of praise for Perisic and highlighted his importance to the team.
“Ivan has behaved very professionally over the past year and he was an important member of our team,” Salihamidzic said. “He played his part in winning the Bundesliga, the DFB Cup and the Champions League. We wish him all the best for the future.”
Head coach Hansi Flick mirrored those sentiments with his own remarks.
Flick said: “I’d like to thank Ivan for his performances and his contribution to winning the treble.
“We were very happy working with him.
“You could see Ivan’s qualities, in particular at the Champions League finals tournament in Lisbon.”
Perisic’s future remains unclear, with Inter now having to decide whether to use him or invite other buyers.
Perisic has two years left on his contract at Inter, whichs runs until 30 June 2022.