The agreement ends a prickly negotiation between the two sides. Neuer, 34, said in April that he was irritated when details about the contract talks were leaked to the media, suggesting the two sides were at an impasse.
"During the weeks of the shutdown for the coronavirus pandemic, I didn't want to make a decision because nobody knew if, when, and how Bundesliga football would continue," Neuer said in a statement Wednesday.
"I look to the future with great optimism. I feel very comfortable and at home in Bavaria."
German media reported in April that negotiations had hit the rocks over Neuer's hefty salary demands, with further reports suggesting Premier League clubs were monitoring the situation closely. Bayern's signing of shot-stopper Alexander Nubel, who will officially join the club from Schalke this summer, also appeared to complicate matters during the negotiation process.
But Bayern sporting director Hasan Salihamidzic eventually confirmed that any issues between the two parties were "clarified internally."
"Since nothing has been leaked since then, I guess the mole has moved on," Salihamidzic said last month.
Neuer, who won the World Cup with Germany in 2014, has captured every major trophy on offer since joining Bayern Munich from Schalke in 2011. He's helped the club hoist seven Bundesliga titles, five domestic cups, and the Champions League trophy in 2013.
Bayern, who returned to action this past weekend after the Bundesliga's pandemic-induced work stoppage, are four points up on Borussia Dortmund as they aim to win their eighth consecutive league title.