Sammer has left his role as technical director with the German Football Association (DFB) to join Bayern with immediate effect.
"I would like to express my thanks to Christian Nerlinger for his work over the past four years at FC Bayern," said Bayern president Uli Hoeness.
"I hope that our good personal relationship continues to remain intact."
Nerlinger was informed of the club's decision to part company at the end of last season, but the announcement was withheld until now to avoid any disturbance to the Germany team's hopes of success at Euro 2012, where Sammer was part of the DFB team.
"I continue to wish FC Bayern all the best imaginable," Nerlinger said on Bayern's website.
"I had a good and intensive time here and will maintain friendly ties with the club."
Sammer, a former European Footballer of the Year who led Dortmund to the Bundesliga title in 2002 and later coached Stuttgart, has worked with the DFB since 2006.
He earlier spent five years as a player with Dortmund, winning the Champions League in 1997.
His departure has been met with regret from the DFB.
"We are deeply sorry to let Matthias Sammer go," said DFB president Wolfgang Niersbach in a statement.
"He has brought a lot of movement into talent development in Germany due to his competence and passion and he has done a great deal of good for the Association with his way of working.
"At the same time, we respect his wish and would not like to stand in the way of his future plans.
"Our close connection to him will remain in the future."
Sammer joins Bayern at a time when they have not won a trophy in two seasons - their longest period without a major triumph since 1994.
Missing out on the Bundesliga title to Dortmund in consecutive seasons led to talks with Nerlinger earlier this summer which, according to the club, "revealed conflicting opinions about the concept for the future of the team".