The Germany legend has backed the starlet to flourish at the Allianz Arena following his summer switch from Borussia Dortmund
The Bayern CEO believes Gotze made the right choice in making the controversial €37 million (£31.5m) summer switch from Borussia Dortmund, insisting the player is in the right surroundings to continue his development.
"He's on the way to world stardom and will make this step at Bayern," Rummenigge told reporters.
"He has the quality to continue to make us successful."
Gotze has yet to make his official Bayern debut as he continues to recover from a hamstring injury, but Rummenigge believes die Roten are well placed to replicate last season's historic success once the full squad is back to fitness.
"In addition to Gotze, we have Javi Martinez, Thiago and [Bastian] Schweinsteiger who are yet to reach their best condition, but when they do, Bayern will win with beautiful football," he said.