Rettig succeeds Bierhoff as national team director at troubled German FA
Four-time world champions Germany, who will host Euro 2024 next year, have been going through their worst run in decades.
Tuesday's 2-1 win over France in their friendly international was only their fifth win in the last 18 matches and came two days after the sacking of coach Hansi Flick.
Bierhoff had resigned in December, days after Germany's second consecutive World Cup group stage exit.
Rettig, who will be the director in charge of the national team as well as the DFB academy, has worked for several Bundesliga clubs and was also the chief executive of the German Football League, in charge of the top two divisions, from 2013-2015.
"I look forward to the challenges," Rettig said in a statement. "(The national teams) are shaped by great successes and currently problems.
"I want to contribute towards making future successes possible again and to improve the direction of the DFB and the performance of its teams in every way."
Germany sacked Flick following their 4-1 home loss to Japan last week, with former national team coach and current DFB official Rudi Voeller taking over for the game against France.
A successor to Flick will be announced in the coming weeks, the DFB has said, prior to Germany's trip to the United States in October.
