The 25 year old was coveted by a number of European heavyweights during the summer, with Bayern always the most likely to secure his services.
However, he decided to remain at Dortmund, who were runners up to their rivals in both the league and the Champions League last term, for the remainder of his contract, which expires at the end of the season.
A four year deal with the European Champions is reportedly in place, and the Poland international can put pen to paper in January.
Lewandowsi has four goals in the league so far last season, taking his total since the beginning of the 2011/12 campaign to an unrivaled fifty.
Dortmund current sit top of the Bundesliga, above Bayern by virtue of goals scored, and Lewandowski is currently the 3/1 favourite to finish the season as the league’s top scorer.