The Germany number one, who arrived at Bayern from Schalke in 2011, signed his new contract on Friday with the club's chairman Karl-Heinz Rummenigge announcing the deal at an emergency general meeting in the evening.
"I find it astonishing and fantastic," said Rummenigge, who praised Neuer for the timing of his decision, just days after a hugely disappointing defeat to Real Madrid in the Champions League.
"This is a sign of his wonderful character that he has said 'I want Bayern Munich forever'. I would like to thank Manuel Neuer for that from the bottom of my heart."
Neuer has been Germany and Bayern's undisputed number one since he arrived from Gelsenkirchen and, barring injury, he will keep goal for his country at the World Cup this summer.
Meanwhile, at Friday's EGM, Karl Hopfner was elected as the new club president, replacing Uli Hoeness, who was sentenced to three and a half years in prison in March.
Hopfner received 99.6 per cent of the votes.
"Many thanks for this overwhelming show of support," Hopfner said. "I am proud to be part of the Bayern family and will always work for the good of Bayern Munich."
Hoeness, who was also present at the EGM prior to commencing his jail term, vowed to return.
"This is not the end," he said. "I have made a huge mistake and I have got to face the consequences, and when I am back, I will not just sit back and retire.
"If I were ever forced to paint a picture of Bayern Munich, then I would have painted them to be the way they are right now - one big family and the club with more members than any other in the world in which every single member really does get a say."