The Germany international goalkeeper has won 10 Bundesliga titles with Bayern, as well as five DFB-Pokals and two Champions Leagues.
Neuer has made 472 appearances since signing from Schalke in 2011, and when his new deal was announced on Monday, expressed his delight at committing to another year in Bavaria.
"I'm very pleased that my journey continues at FC Bayern," he told the club's website. "We'll have a very good team again with which we can play for every title.
"As a goalkeeper, captain and leader, I want to be the support and a key factor in our big goals. We want to extend our title record and compete again for the DFB Cup and Champions League."
Of goalkeepers who played at least 20 games in the Bundesliga in the 2021-22 season, no one conceded fewer than Neuer's 26 goals (in 28 games).
Former Bayern stopper Oliver Kahn, who is now the club's chief executive, also spoke of his pleasure at the news.
"Manuel Neuer is the best goalkeeper in the world and has been setting the standard around the world for years," he said. "It's a huge achievement to be so consistently world-class for such a long time.
"We're very happy to have extended his contract. Manuel is a defining figure in the history of FC Bayern."