Munich, the last German Summer Games host 54 years ago, was one of three original candidate cities for the vote, along with Cologne-Rhine-Ruhr and Berlin, but the capital pulled the plug two days before the vote following local elections last week.
"The winner is Munich," German President Frank-Walter Steinmeier said at the DOSB general assembly after being handed the envelope with the winning bid.
"If we go to the starting line as Team Germany, then we have good chance to become Olympic hosts," he had earlier said.
Munich's bid, which includes use of the Olympic park built for the 1972 Games, enjoys strong local support.
It will face stiff competition, especially for 2036, with the IOC having said more than 10 cities or countries had expressed an interest, among them Indonesia, India, South Africa, Chile's Santiago as well as Doha, Saudi Arabia and Turkey.
Los Angeles will host the 2028 Olympics and Brisbane, Australia will stage the 2032 edition.
There is no date for a decision by the International Olympic Committee, which has changed its bidding rules in recent years, with several stages of dialogue with interested parties resulting in one preferred candidate to be put to the vote.
The IOC usually awards the Games about seven years in advance.
Germany last hosted the Summer Olympics in 1972 in the Bavarian capital, which were marred when Palestinians from the Black September militant group took members of the Israeli Olympic team hostage. Eleven Israelis, a German policeman and five of the Palestinian gunmen died after a stand-off at the Olympic village and the nearby Furstenfeldbruck airfield.
Previous efforts by Germany to land Summer or Winter Games failed mostly at the first hurdle, with local referendums opposing such plans over their size and cost, as was the case for Hamburg, which was planning a bid for 2024.
Munich had also unsuccessfully bid for the 2018 Olympics, finishing second behind Pyeongchang in South Korea.
