The Germany legend, the all-time leading goalscorer in World Cup history and for his country, will take over the Bavarian giants' youth team for the 2018-19 season.
Klose represented Bayern between 2007 and 2011, winning two domestic doubles before moving on to Lazio, where he ended his career.
"I'm really looking forward to this role at Bayern's academy," 2014 World Cup winner Klose said.
"I'll give everything I can to justify the faith placed in to me to lead the development of these young players."
Bayern also confirmed 17-year-old Franck Evina has signed a three-year professional contract.
Evina has started two Bundesliga games this season and sporting director Hasan Salihamidzic hailed the teenager's potential.
"Franck is a quick forward who has enormous athletic qualities," said Salihamidzic. "We're very happy we've secured his services over the long term, and we aim to further promote his good progress."
Evina added: "It's a great honour to get this chance at Bayern.
"I want to continue to learn a lot in the next few years and want to repay the club's faith with good performances."