The German champions' chairman believes the fans will be excited to see the Poland striker on his way to Munich from Borussia Dortmund this summer
The 25-year-old forward will leave Borussia Dortmund when his contract expires in the close-season to link up with the Bundesliga champions.
The Poland international has scored 20 goals or more in his last three Bundesliga seasons and also provides a wealth of European experience for coach Pep Guardiola.
Rummenigge told the club's official website: "Robert is a world-class striker and Bayern fans everywhere can look forward to seeing him play for us.
"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."
Rummenigge confirmed the club are still keen to keep midfielder Toni Kroos, who has been linked with Manchester United, while suggesting there willl not be many major moves in the transfer market this summer.
He continued: "As I've always said, our aim is to agree a contract extension with Kroos - and that still applies. If we can't, we'll have to think about other options.
"We fundamentally have a very good team and the squad is not particularly old. None of our players are due for retirement, so we can be very relaxed and calm as we survey the future.
"We are still watching the transfer market very closely. Fortunately our finances are extremely solid and we have no problem with Financial Fair Play.
"There won't be any serious activity in the transfer market until the World Cup gets going. Relatively little will happen before then."