"We have been in agreement with the (new) club for some time now," he told Sport Bild magazine.
"I have informed the people in charge (at Dortmund) and I assume that all will now be cleared up and I can join the club of my wish this summer."
"This would be the best thing for all sides," said the 25-year-old, who grabbed headlines by scoring four goals against Real Madrid in the Champions League semi-final first leg.
Lewandowski, second-top scorer in the Bundesliga last season and widely expected to join European and German champions Bayern Munich, has refused to sign an extension to his current contract that runs out in 2014.
Bayern coach Jupp Heynckes said after their 2-1 Champions League win over Dortmund at Wembley stadium last month that a deal for the striker was only a matter of time.
The forward, who won consecutive Bundesliga titles with Dortmund in 2011 and 2012 as well as last year's German Cup, joined the Bundesliga side in 2010 from Polish club Lech Poznan.
Bayern, who last season became the first German side to win the treble, have already signed talented playmaker Mario Goetze from Dortmund in a deal put at 37 million euros (£31.5 million) by German media.