"I'm very glad to be back in Germany", he said.
Following the health checks, the 30-year-old winger sent a message to Bayern fans. Their chances of signing Manchester City's Leroy Sane this summer ended after he suffered a serious knee injury in the Premier League champions' Community Shield victory over Liverpool.More news: Argentines lose patience with economy and Macri
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Perisic starred for Croatia in the FIFA World Cup a year ago in Russian Federation, during a tournament where his nation made it to the final, only to lose to France. Bayern are one of the biggest clubs in Europe.
Sporting director Hasan Salihamidzic added: 'Ivan will help us from the start with his extensive experience at a top global level.
"He is technically gifted and flexible in attack". "We don't want to just win the league and cup, we also want to attack the Champions League", said Perisic.
"I am sure that Ivan will integrate quickly as he already knows the Bundesliga and Niko Kovac", added Salihamidzic.