Guardiola replaced Jupp Heynckes at the helm of Bayern after the veteran boss had led the German giants to four trophies, including the Champions League, in the previous season.
"What impresses me the most about him is his obsession and meticulousness. It's totally fascinating," Rummenigge told Sport1.de.
"It's no coincidence that he's so successful with Bayern Munich. After we won the treble, everybody felt that things could carry on that way, or that maybe we would drop down one or two steps, but Pep has managed to take us one or two steps higher.
"The team is even more stable, play with more variety and have reached a greater level than last season. We're incredibly happy with him. He's settled in fantastically well."
Bayern have made an unbeaten start to the Bundesliga campaign, dropping just four points in their opening 15 games on their way to the top of the table.