Klose has signed a one-year contract and will begin his role from July 1.
The 41-year-old has been a coach at Bayern’s youth side for the last two years, having retired from professional football in 2016.
Klose spent four years as a player at Bayern Munich between 2007 and 2011, making 150 appearances in all competitions and scoring 53 goals. He won two Bundesliga titles and two German cups during his time in Bavaria.
Flick was assistant to Joachim Low when Klose scored twice at the 2014 FIFA World Cup in Brazil to help Germany win football’s greatest prize.
"Hansi Flick and I have known each other very well since our years together with the German national team, we trust each other both professionally and personally," Klose said in a club statement.
"For me, this is the next step in my career as a coach. I hope that with my experience I can make an important contribution to Bayern achieving its sporting goals."
Flick, who has tied down current assistant Danny Rohl until 2023, added: "With his experience as a former professional at the highest international level, Miro is the perfect addition to our team of trainers.
"We have known and esteemed each other for a long time and have had great success together with the national team. The fact that Danny Rohl will remain with us in the long term is also great news for my team and me."
Klose is the top scorer in the history of the FIFA World Cup with 16 goals.
