The versatile 18-year-old player has been closely linked with the Bundesliga record champions in recent weeks, and on Friday put pen to paper on a three-year contract
Weiser's previous deal was set to expire in 2013, but Koln accepted an undisclosed fee believed to be in the region of €500,000 in exchange for his release.
"We are pleased that in Mitchell Weiser and Emre Can we have two of the most talented young German players in our
senior squad," Bayern sporting director Christian Nerlinger said in response to the signing.
Weiser, who can play in defence and midfield on either flank, was thrilled with having completed his move.
"If you can as a junior player become a professional at Bayern, you have to take on the challenge. This is a huge opportunity for me," he said.
Weiser and Can played together last season in the Germany Under-17 squad, since which time the versatile wide player has seen his stock rise considerably.
Weiser made his Bundesliga debut in February as a substitute in Koln's 2-0 derby defeat to Leverkusen.