The 27-year-old leaves Melbourne Victory to link up with the iconic club who play in the Frauen-Bundesliga, the top division in Germany.
Gielnik, who has played 31 times for the national team, said the move was a dream come to.
"I'm excited. It is the dream of every footballer to play for a top club like Bayern Munich. As a striker, I now want to score as many goals as I can for my new club," she told the Bayern Munich website.
"I want to win the Bundesliga and the Champions League with this great team. These are big goals, I know, but that's exactly what I'm going to fight for and give everything."
The Aussie clearly impressed Bayern Munich's hierarchy with her FIFA Women's World Cup performances in France.
"We are happy that Emily has decided for Bayern. She has a good physique and speed and can play in the offensive area on all positions. This type of player was missing us in the squad," Bayern head coach Jens Scheuer said.
"We've been watching Emily for a while. At the 2019 World Cup, she once again came to the fore with the Australian national team, so we wanted to make a commitment after the opportunity arose."
Gielnik has previously had stints with Liverpool, Ottawa Fury, Urawa Red Diamonds and Brisbane Roar.
