The former Barcelona coach will take over from Jupp Heynckes as Die Roten boss next season and the club CEO feels that the Spaniard will prove to be an inspired appointment at the newly crowned Bundesliga champions.
"He respects the culture and philosophy of Bayern and this is what could make his stint a success," Rummenigge told the Times of India.
"Pep used to get Barcelona to play Rayo Vallecano and Real Madrid with equal focus, that's the kind of mentality he has.
"With him, we can write an important part of history next year. He's everything but arrogant. He respects the Bavarian culture and doesn't want to change the philosophy."
Bayern travel to Juventus for the second leg of their Champions League quarter-final tie tonight leading 2-0 from the first leg played last week.