The Bayern official says the Spaniard was the ideal choice to lead the Bavarians and feels that Barcelona are still the benchmark in Europe
Guardiola was handed the reins following the departure of Jupp Heynckes, who led Bayern to an historic treble in 2012-13.
But Rummenigge thinks Guardiola can still take the club to another level, with the Bavarians on course to defend their three titles this term.
"We had a very successful season last year, winning the treble. But with the arrival of Pep came something additional with quality, I’d say," the CEO told Sports Illustrated.
"I’d say he’s born to work in favour of Bayern. I’m watching sometimes 15 to 20 minutes in training sessions, and this quality he’s giving in favour of the team is impressive to all of us.
"He’s a fantastic coach and guy. We believe it’s a fantastic story, what he is doing."
Despite their Champions League triumph last season, Rummenigge admits Barcelona and representatives from the Premier League still have the lead in Europe.
"Barcelona are a very good example, a kind of benchmark for us. We try to follow them. Regarding the five-year Uefa ranking, we are number two. Barcelona is still number one," he continued.
"[Upcoming Champions League opponents] Arsenal are doing well this year in the Premier League, so it looks like they’re a bit reborn, a kind of comeback to the old times.
"In the next five to seven years I’d say the Premier League will remain number one. Maybe the Bundesliga is on a good path to be number two, but the Premier League has a certain advantage."