Guardiola signed a three-year deal with Bayern on Wednesday that will see him take over the record German champions in July.
In doing so Rummenigge believes Guardiola, who turns 42 on Friday, turned down more lucrative offers. "If it were purely down to money, then Bayern would have had no chance," he said.
Guardiola was a wanted man since stepping down as coach of Barcelona last summer. He then decided to take a one-year sabbatical, yet six months into that break, speculation about where he would return had hit fever pitch.
His decision to join Bayern may raise a few eyebrows, but Rummenigge believes it was a pondered choice and that the Catalan was more attracted to what Bayern and German football had to offer.
"I think he was impressed with our overall concept," he said.
"Of course he'll be earning a few euros here too, but if finances had been the defining factor, then he would not be coming here on 1 July. He was pleased with the way we have established a financial independence."
Bayern are nevertheless Germany's richest football club and, after breaking the league's transfer record by splashing out 40 million euros on Javi Martinez last August, a host of current Barcelona players are inevitably going to be linked with a move to Munich.
There is still money in the bank to fund such arrivals and Rummenigge is not ruling out big name signings following Guardiola's arrival in the summer.
"Of course he is a coach with great charisma and there are players who would love to work with a coach like him," he said at a press conference in Munich.