The England captain's previous agreement was due to expire in 2027, but the new deal will keep him at the Allianz Arena for another two seasons.
Kane has scored 156 goals in 161 competitive appearances since joining Bayern from Tottenham Hotspur in 2023, establishing himself as one of the most prolific forwards in European football.
His extraordinary form helped him claim the Ballon d'Or last month, ahead of Kylian Mbappe and Lamine Yamal, after a season in which he scored 73 goals for club and country.
The 33-year-old has also enjoyed considerable team success in Germany, winning two Bundesliga titles, the DFB Cup and two Franz Beckenbauer Supercups since his arrival.
Kane was delighted to extend his stay, explaining that he and his family have settled into life in Munich.
"I feel right at home at FC Bayern. I love the club, the fans and the city of Munich," he said.
"We have a fantastic team and, in Vincent Kompany, a fantastic manager. It makes me very proud to be part of this club.
"My whole family is very happy here. I was keen to stay. I'm now looking forward to the future and I want to win many more titles with this great club."
Bayern president Herbert Hainer welcomed the agreement, describing Kane's contribution as an important part of the club's recent history.
The extension also ends any immediate prospect of a return to the Premier League, where Kane had been linked with a move as he approached the final stages of his previous contract.
A potential return to England would have offered the striker an opportunity to pursue Alan Shearer's Premier League goalscoring record, but he has instead chosen to continue his career in Germany.
Reports in Germany suggest the new agreement makes Kane one of the highest-paid players in European football, with his annual salary believed to be around €25 million before bonuses. Bayern have not disclosed the financial terms.
Kane's commitment gives Kompany a major foundation for the coming seasons as Bayern look to build on their domestic success and pursue the Champions League.