Bayern and the Dutch Football Association (KNVB) have been quarrelling ever since 27-year-old Robben returned from the World Cup in South Africa last July with an aggravated thigh muscle injury.
It kept him out of football until January and Bayern has now settled the matter with a friendly against the Dutch national team on May 22, 2012.
"We are glad to have settled the issue," said Bayern's chairman Karl-Heinz Rummenigge in a statement. "It is good for the football community that we have found a fair and satisfactory solution."
The Dutch are likely to use the match as a warm-up for the Euro 2012 tournament set to be held in the Ukraine and Poland and which starts on June 8, 2012 in Warsaw.
"We have accepted that we could not reach an agreement in general discussions, so it was best to settle our differences and to search for a viable solution for both sides," said Bert van Oostveen, the CEO of the KNVB.
"We have done that, we are satisfied with the result and we look forward to a great friendly match in Munich."
Neither side revealed how the proceeds of the game would be divided.