Lewandowski, whose contract at Dortmund runs to 2014, had refused to sign an extension late last season and had said he hoped to be joining his "club of choice" very soon.
After a months-long transfer saga and with Lewandowski set to become the second Dortmund player to be poached by rivals Bayern after Mario Goetze, Dortmund blocked the move which would have brought in millions of euros.
"I will give everything I've got for Dortmund," Lewandowski told Bild newspaper. "It does not matter what happened. I am not interested about that on the pitch."
The Poland international enjoyed a sensational season, scoring 24 league goals and adding another 10 in the Champions League, including four in one game against Real Madrid.
Dortmund, who lost out to Bayern in all three competitions last season, will not receive a transfer fee if Lewandowski leaves as a free agent after his deal expires next year.
"When I am out on the pitch then Dortmund is all I think about. I want to give it all I got and be successful," he said.
Lewandowski has already bagged his first silverware of the season, Dortmund winning the German Super Cup title by beating Bayern 4-2 last week.
The 24-year-old showed no signs of disappointment over the failed transfer, setting up his team's first goal.
"I hope this was not the last title," he said.
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