GOAL - Guy Atkinson
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.
Head coach Niko Kovac has been in the market for at least one new wide forward following the departures of Franck Ribery and Arjen Robben at the end of the 2018-19 campaign.
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.
He has made 82 appearances for Croatia and starred at the 2018 World Cup, scoring in the semi-final against England and in the final defeat to France.
"I am very happy to be back in Germany," Perisic told Bayern's official website.
"Bayern is one of the biggest clubs in Europe. We want to attack not only in the Bundesliga and in the DFB-Pokal, but also in the Champions League."
Bayern's sporting director Hasan Salihamidzic added: "Ivan will help us with his many years of experience at an international top level immediately.
"He is technically strong and flexible in attack. I'm sure Ivan will integrate quickly as he already knows the Bundesliga and our coach Niko Kovac well."