The Poland striker's long-anticipated move to Bayern was confirmed on Saturday when he put pen to paper on a five-year deal with Dortmund's Bundesliga rivals from the start of next season.
Until then, however, he is committed to the Westphalians and has vowed to help them reach their goals for the season.
"Dear BVB fans, I would like to send you a short message," he wrote on the Dortmund website.
"We have half a year ahead of us in which we have several objectives which we want to reach together.
"Even if there are going to be some fans among you who do not agree with my decision, I hope you still give me your support.
"I will definitely give everything for BVB!"
Lewandowski treads the same path as Mario Gotze last summer, although the timing of his announcement, and the fact a move was widely expected since he had already told Dortmund he would not be extending his contract, means he may escape the same kind of treatment Gotze received.
Gotze's transfer to Bayern was leaked on the eve of Dortmund's Champions League semi-final tie with Real Madrid and the Germany international subsequently incurred the wrath of the Dortmund faithful.