However, The German’s side have the luxury of buying the Croatian International at the end of the season, as part of the deal.
In January, the Gunners made an approach to sign the 30-year old, during that time Manchester United was also in talks to sign him.
Perisic was amongst the players of Borussia Dortmund and Wolfsburg before he moved in Inter Milan in 2015.
He was also part of the Croatian National team which came second at the 2018 World Cup after losing to France.
“I’m very glad to be back in Germany. Bayern are one of the biggest clubs in Europe.
“We want to go on the attack, not only in the Bundesliga and the DFB Cup, but also in the Champions League.” He said to the media.