Hoeness, a former Bayern player in the 1970s who also won the 1972 European championship and 1974 World Cup with Germany, was elected at the club's annual general meeting in Munich amid roaring applause.
Beckenbauer, captain of the hugely successful Bayern and Germany teams in the 1970s and who also coached Germany to their 1990 World Cup victory, becomes honorary president in a move announced a year ago.
Long regarded as the person who revolutionised football marketing in Germany when he took over in 1979, Hoeness said the club's finances were as healthy as ever.
"My successors have a golden future as we are financially independent," the 57-year-old Hoeness told the meeting. "Which other top club can claim that?"
Hoeness joined Bayern as a gifted 18-year-old attacking midfielder and in a hugely successful eight-year spell won every single major title for club and country, including three German championships and three European Cups.
When he took over as manager in 1979, the Bavarian club was in debt.
He leaves his position having steered Bayern to unprecedented financial growth and having seen them crowned German champions 16 times since 1979. They also won the 2001 Champions League.
Hoeness helped engineer the club's successful sponsorship and marketing plans as well as the construction of their 69,000-capacity Allianz Arena, which belongs to Bayern.
As a going-away present Hoeness sealed a 90 million euro deal with German car maker Audi on Thursday for the purchase of 9.09 percent of the club's shares.
A darling among Bayern fans, Hoeness often angered others with his vocal support for the club.
He has been replaced on the Bayern bench this season by Christian Nerlinger, who took over as sports director.
