Guardiola was announced as Jupp Heynckes' successor in January before taking the helm at the Allianz Arena in June.
Heynckes enjoyed an unprecedented final season in charge as Bayern became the first German side in history to win the treble, securing the Bundesliga, DFB Pokal and UEFA Champions League.
Rummenigge is confident that Guardiola's presence at the club will enable them to maintain their success and has praised the former Barcelona boss for his impact so far.
"I've seen the incredible energy Pep puts in," he told the club's official website.
"It makes me want to go out there and join in myself. He has fantastic ideas, but he's also a meticulous hard worker. Nothing happens by chance, every last detail is planned.
"I'm utterly convinced we needed something new after last season. I've been through it myself, in 1975, 1976 and 2001. When you've had such great success, you're naturally inclined to take it a little easier – and that's an immediate step backwards.
"It's no coincidence that we won nothing in 2001-02, and played nothing like the fantastic football of the previous season. But every player has to prove himself all over again for the new coach.
"Thanks to the high quality in the squad, none of them can take it easy. Any player who's become complacent has a hungry man right behind him."
Bayern have brought in midfielders Mario Goetze and Thiago Alcantara so far during the close-season.
Thiago reportedly rejected Manchester United to join Bayern and Rummenigge is delighted with what he has seen from the 22-year-old.
"You can see he's a complete player," he added.
"He has exceptionally good technique, and he's completely taken on board our tactics, partly due to the fact he's already worked under Pep. I think we're going to get a lot out of Thiago."
