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 is keen to see Lewandowski represent Bayern and has praised the striker's work-rate.
He told Bayern'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.
"And I've also heard he's a model pro (professional)."
One player who continues to be linked with a switch away from Munich is midfielder Toni Kroos.
Kroos has reportedly been a long-time target of Premier League outfit Manchester United but Rummenigge said the club are still keen on tying him down to a new deal.
"As I've always said, our aim is to agree a contract extension, and that still applies," he added.
"If we can't, we'll have to think about other options."
Rummenigge also said that Bayern - who have already announced the signings of Lewandowski and midfielder Sebastian Rode - will be keeping a close eye on the transfer market.
And he hinted at further arrivals following the conclusion of the FIFA World Cup in Brazil.
"We fundamentally have a very good team, nor is the squad particularly old," he continued.
"None of our players is due for retirement. We can be very relaxed and calm as we survey the future.
"But we're 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."
