Bayern had looked set to make a move for Leroy Sane throughout the transfer window, but any possibility of signing the Manchester City winger was ended when the 23-year-old sustained knee ligament damage in the Community Shield clash with Liverpool on August 4.
The move for Perisic was made swiftly, though not all Bayern fans have been pleased by the transfer, with coach Niko Kovac hitting out at suggestions the Croatia forward was not of the standard required.
"It happened really quickly. Everybody knows what happened [with Sane], and I hope he recovers well and quickly," Perisic told a news conference ahead of Bayern's opening Bundesliga fixture against Hertha Berlin on Friday.
"But when they called me, I took only a few hours to take my decision with my family. When a club like Bayern call, you cannot say no.
"That's the reason I’m here. I want to do the best here every day, each game and I hope it's going to be a successful year."
Perisic will have to compete with Kingsley Coman, Serge Gnabry and youngster Alphonso Davies for a spot in Kovac's side, though at 30, he adds some more experience to Bayern's attack following the departures of Arjen Robben and Franck Ribery.
"I'm coming here to be part of the team, and to play. There are a lot of games, and at this level you cannot play all the games," Perisic said.
"We need everybody, at least 17, 18 players if you want to be on top. You know during the season there's going to be injuries, so we'll need everybody."
Perisic scored eight Serie A goals for Inter, who he joined in 2015, last term, though believes his form was hindered due to a lack of rest following Croatia's run to the World Cup final.
"The last year was a really difficult one after the final. I had not even 20 days for recovery," he added.
"When I returned to Inter I was back in the side for the first game of Serie A. That was the reason the season was many ups and many downs.
"When you look at all the players who played in the final, you will see maybe one or two that had a really good season.
"But this season I had a really good pre-season with Inter, with the new coach [Antonio] Conte he is a really hard worker, and it's going to help me a lot here."