Eberl, a former Bayern player, has joined on a contract till June 2027 and will take charge on March 1st, the club said on Monday.
He served as the director of sport at Borussia Monchengladbach for 14 years before joining Leipzig in 2022. Leipzig sacked him in September after media speculations linked him to a move to Bayern.
"Not only does he have decades of experience in football management, he also started playing soccer at FC Bayern and turned professional here," Herbert Hainer, chairman of Bayern's supervisory board, said in a statement.
"We are convinced that he will successfully shape the future of this club."
Eberl said he would approach his job with "a lot of respect and humility."
"I spent my entire childhood and youth at FC Bayern and in Munich, so it is something special for me to now return in a new role to the club where it all began," he added.
Bayern, who trail Bundesliga leaders Bayer Leverkusen by eight points, visit Freiburg on Friday.
