Lewandowski, who has scored five goals in two Bundesliga games this term, has committed his future to the club through to 2023.
The 31-year-old could therefore spend the rest of his career at the Allianz Arena, having established his place as one of the world's top strikers since joining from Bundesliga rivals Borussia Dortmund in 2014.
Lewandowski's new contract is a two-year extension and the striker is thrilled to have secured new terms.
"Bayern has become my sporting home," he told the club's official website. "Besides, my family and I are happily settled in Munich.
"I'm convinced we'll achieve a lot in the next few years. Bayern are one of the three biggest clubs in the world, and we have an outstanding team. I'm proud to be part of this club."