Davies has won nine caps for Canada, scoring three goals and assisting on four.
Those numbers caught the attention of the German champions Bayern, who in July paid $22 million for the then 17-year-old.
Davies, who turned 18 in November, will join Bayern in January when the international transfer window opens.
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"He has been a stand-out performer for club and country and that is just a consistent reality now for Alphonso Davies," said John Herdman, head coach of Canada's national men's team, in a statement.
"For club, he picked up many an accolade, culminating with what looks like one of the biggest signings our country has ever seen.
"For Canada, every time he has been asked to take a responsibility and support the team, even playing out of position, he has shown his character."
(Reporting by Steve Keating in Toronto; Editing by Ian Chadband)
