Guardiola took over from Juup Heynckes at the start of the 2013-14 campaign, and will have been aware of the act he was following after Heynckes delivered the Bundesliga title, DFB Pokal and UEFA Champions League in his final season at the helm.
Former Barcelona coach Guardiola could not quite replicate that success, exiting the Champions League at the semi-final stage having been thrashed 5-0 on aggregate by eventual winners Real Madrid.
Bayern did continue to dominate the domestic scene, however, claiming a league and cup double, and Rummenigge paid tribute to the manner in which Guardiola has made his mark at the Bavarian club.
"He's shown the same level of quality as he did at Barcelona," the chairman told the club's official website.
"Pep is a wonderful coach with a clear philosophy, a clear plan. We're really happy with him. We have to thank the dear Lord he sent Pep Guardiola to us in Munich.
"After winning the treble you might tend to think you don't need to change anything and all changes are wrong. But Pep has changed quite a few things. And all the changes he made were right.
"He got rid of the two defensive midfielders, he put Philipp Lahm in the holding role, the team played higher up the pitch and they pressed more than in the previous season...he set the team new challenges.
"Players like Philipp Lahm, Arjen Robben and Manuel Neuer have repeatedly told me how much the squad enjoy the new regime. We've also played a different quality of football in this campaign."
The decision to change Lahm's role was lauded by Rummenigge, who also revealed that Bayern's European disappointment still irked Guardiola.
"It was a brilliant decision," he said. "We had arguably the best right-back in the world - and moving him into defensive midfield improved the quality of the team.
"Philipp enjoys playing in his new role and he’s incredibly clever and intelligent in that position.
"I think the only thing that annoys him is not winning the Champions League. He's incredibly ambitious."
