The 25-year-old will officially sign for the club when his Borussia Dortmund contract expires this summer, and Rummenigge is excited by the prospect of seeing the Polish forward in action for the Bundesliga champions.
"Robert is a world-class striker and Bayern fans everywhere can look forward to seeing him play for us," the Bayern CEO told the club's official website.
"He scored lots of goals for Borussia Dortmund. He gets through a great deal of work for the team and he uses his physique to optimal effect, even though he's not actually that big. I have also heard he is a model professional."
Lewandowski scored 28 goals in all competitions this season.