Bayern, long-time admirers of the Schalke talisman, also announced the signing of Brazilian defender Rafinha from Italy's Genoa on a three-year deal.
"The transfer contract with Schalke was signed today. Manuel Neuer will join from July 1," Bayern said in a statement before adding that the player would undergo a medical after Germany's upcoming Euro 2012 qualifiers.
The 25-year-old, who has been attached to Schalke since he was five, helped them win the German Cup this season and reach the Champions League semi-finals.
"I am really looking forward to this big and exciting challenge that is Bayern," said Neuer after ending months of speculation about his future.
"I will be playing at the same club as a lot of my team mates in the national team so it will not really be foreign territory for me."
He can, however, expect some Bayern fans to be angry at the move as they had repeatedly tried to block the transfer of a player they see as the face of league rivals Schalke.
Ralf Faehrmann, 22, who left Eintracht Frankfurt as a free agent following their relegation from the Bundesliga, replaced him at Schalke, a club he made his Bundesliga debut for in 2008.
Neuer is considered one of the best keepers in Europe and was linked with several top clubs including Manchester United.
"We decided to accept the Bayern offer because this is the best thing for the club under the circumstances," said Schalke sports director Horst Heldt, who said every Schalke fan would be hurt by Neuer's departure.
Bayern, who will play in the Champions League qualifying round next season after finishing third in the Bundesliga, said Rafinha, who also played for Schalke until last year, had signed a three-year deal.
Schalke, who claimed a Europa League spot thanks to their German Cup triumph, finished 14th in the Bundesliga.
