The Bundesliga champions fought off competition from Real Madrid, Liverpool and Paris St Germain to sign the fleet-footed 17-year-old on Thursday, July 26.
The fee — $16.4m — could turn out to be a real bargain, according to many football pundits on social media.
Davies, who was born in a refugee camp in Ghana, came to Canada at the age of five and grew up in the frozen wastes of Edmonton, Alberta.
His footballing skills impressed Vancouver Whitecaps and he has wowed crowds in the MLS with his dazzling footwork, reminiscent of Diego Maradona or Pele.
"As a kid, you dream about this moment and I'm happy it came through. Now it's time to continue working, I have to give everything to make the most of this opportunity," Davies told reporters.
Davies has signed a five-year deal with Bayern, having been tipped for the top by German midfield legend Bastian Schweinsteiger.
"He has great potential with his speed and technique. If he works hard, especially on his defence, he can, of course, make it in Europe," Schweinsteiger, told the German daily Bild.
"They opened my eyes and explained everything very well," said Davies of Bayern's offer.
Best Player To Come Out Of Canada Since Owen Hargreaves
He follows in the footsteps of Calgary-born Owen Hargreaves, who helped Bayern win the 2001 Champions League title before joining Manchester United and playing for England.
Davies though will be representing Canada, having been called into the senior squad the same day he became a citizen — June 6, 2017.
In July last year, when he was just 16, he made his international debut and scored twice as Canada beat French Guiana 4-2.
🗣️ @Brazzo: "@AlphonsoDavies is a huge talent. At just 17, he has a bright future ahead of him. Alphonso is very talented and it comes as no surprise that many other top clubs were after him." #MisSanMia pic.twitter.com/5fLu7Kbbf8— FC Bayern English (@FCBayernEN) 25 July 2018
The teenager, who turns 18 in November, will remain at Vancouver until the end of the MLS season and will join Bayern in January.
He has scored three goals in 20 games in the MLS as well as six assists.
'He Has A Great Future'
"He is a young, talented player that many clubs in Europe wanted. He is a player who will definitely have a great future, if he stays healthy and develops in the way both he and we expect him to," said Bayern's head coach Niko Kovac.
Alphonso Davies' transfer to Bayern Munich makes him the most expensive MLS player of all time.— FOX Soccer (@FOXSoccer) 25 July 2018
Not bad for a 17-year-old 👏👏 pic.twitter.com/HAVA1aJK3x
Bayern are investing heavily in young players for the future.
Earlier this week Luxembourg international Ryan Johansson, 17, and American defender Chris Richards, 18, featured in a Bayern side which lost to Juventus in a pre-season friendly in Philadelphia.
Ironically Liberia — where Davies was born — has a president, George Weah, who was once a huge football star.
Weah scored 193 goals in 411 games — most notably for AC Milan — and was playing for Manchester City when Davies was born.
Up to 300,000 people died in the Second Liberian Civil War, which began in 1999 and ended in 2003 when Charles Taylor resigned as President. He was later tried for war crimes at an international tribunal and was jailed for 50 years in 2012.