The Bavarian giants moved for Perisic after failing to seal moves for top targets Callum Hudson-Odoi and Leroy Sane.
He said in July on the back of a 1-0 International Champions Cup defeat to Manchester United: "We're working with him, but his response isn't positive".
The 30-year-old has always been linked with a move away from Serie A side Inter and is expected to join Bayern on an initial season-long loan move, with an option to make the deal permanent next year.
He has 23 goals in 82 starts with Croatia, who came second in last year's World Cup in Russian Federation.
"Everybody knows that Bayern is a really big club".
Sporting director Hasan Salihamidzic added: 'Ivan will help us from the start with his extensive experience at a top global level.
"We want to go on the attack, not only in the Bundesliga and the DFB Cup, but also in the Champions League".
"He is technically gifted and flexible in attack".