The Polish forward, whose new deal is expected to run until 2023 was thrilled to have extended his stay with the Bavarians.
"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."
Since arriving from Borussia Dortmund in 2014, the goal poacher has established himself as one of the finest centre-forwards in the sport with his impressive performances.
Lewandowski has bulged the net five times in two Bundesliga games for the new season.
At age 31, and renewing his contract which will expire when he turns 34 years, Lewandowski could therefore spend the rest of his career at the Allianz Arena.
After several speculations linking Lewandowski with Real Madrid this summer, the fearful forward has ended all advances by any potential suitors after committing himself to Niko Kovac’s side.
With the arrival of Philippe Coutinho and Ivan Perisic as possible replacements for departed veterans Frank Ribery and Arjen Robben, Lewandowski is expected to partner well with the creative midfielders for the side to re-gain their lost European status.
Bayern CEO Karl-Heinz Rummenigge also expressed his delight for their first-choice striker to prolong his stay with the club
"For me, Robert is the best centre-forward in the world and has been a mainstay of our team for years.
"Therefore, we are very happy that he will play at for Bayern for a long time to come. We are confident that with Robert, we will achieve our ambitious goals in the coming season and in the years to come."
