Guardiola had a tough act to follow with Heynckes winning four trophies last season, but Rummenigge has been bowled over with the job he has done in just five months at the helm.
"What impresses me the most about him is his obsession and meticulousness," Rummenigge told Sport1.de. "It's totally fascinating.
"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's dominance is not a concern for Rummenigge, though, who feels the gap between his side and the rest will never reach proportions of Celtic's supremacy of Scottish football.
Nor is the Bundesliga at risk of becoming like Barcelona and Real Madrid's duopoly in Spain with Bayer Leverkusen and Borussia Dortmund ensuring "more of an English Premier League situation" with several clubs vying for the title.
"The fact is we have three teams at the top, and that's something the Bundesliga rivals can be relaxed about," he added.