The 30-year-old joined Inter in 2015 and has been a regular starter during his four years at San Siro, scoring eight goals in Serie A last term.
He will provide competition to Serge Gnabry and Kingsley Coman at the Allianz Arena and could be included in Bayern’s opening league game against Hertha Berlin on Friday.
Bayern’s hopes of signing Manchester City’s Leroy Sane in this transfer window were effectively scuppered last week following the news he will be out for six to seven months after suffering an anterior cruciate ligament injury to his right knee.
Perisic has previously played in the Bundesliga, initially for Borussia Dortmund before joining Wolfsburg midway through the 2012-13 season. He won the domestic double with Dortmund in 2012 and went on to win another DFB-Pokal and DFL-Supercup with the Wolves.
“I am very happy to be back in Germany,” Perisic told Bayern’s official website.
Bayern’s sporting director Hasan Salihamidzic added: “Ivan will help us with his many years of experience at an international top-level immediately.