Lewandowski was desperate to leave the Champions League runners-up to join treble winners Bayern Munich but the deal fell through after Dortmund blocked the transfer, saying he had a contract until 2014.
The striker has also been linked with moves to Chelsea and Manchester United.
A bitter war of words ensued between the two sides, raising concerns over his commitment to Dortmund in his final year of his contract.
"The situation is now that I will stay in Dortmund for one more year," Lewandowski told sport bild magazine. "We have put aside all disagreements and have cleared the air. There were mistakes made but the case is closed."
"I had a different starting point. I thought I was allowed to transfer. I was then disappointed and angry. But now everything is calm. I have always said I would respect my contract."
Dortmund also said they gave the forward an unspecified pay hike last week based on last season's performances.
"It is true that we have adapted his remunerations to his sporting contribution," Dortmund CEO Hans-Joachim Watzke said, without giving any details on the rise of the forward's annual salary. "We had intended for months to do that."
German media reported his salary was up from 1.5 million euros (£1.3 million) to 5 million (£4.3 million) annually.
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.
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