"I'm really pleased that the discussions have come to a positive conclusion and that I'll be staying at Bayern for several more years," said Lewandowski, "We've got big targets together."
Club chairman Karl-Heinz Rummenigge was also pleased to have successfully completed negotiations with the star striker. "I'm delighted that we've been able to come to a long-term agreement with Robert Lewandowski, one of the best strikers in the world. This means that we've ensured that one of the key players in our squad will continue wearing the FC Bayern kit over the coming years."
Lewandowski has won back-to-back Bundesliga titles since joining from Borussia Dortmund in 2014, plundering a league-high 30 goals as the club sealed a record fourth consecutive top-flight triumph last term.
The Poland national team captain currently sits third in the goalscoring charts in the current campaign having scored 11 times in 14 appearances, including a brace in Bayern's 5-0 thrashing of VfL Wolfsburg on Matchday 15.
Watch: Relive Bayern's defeat of Wolfsburg