Their unanimous decision will be put to the DOSB General Assembly in Dresden on December 6th.
Germany has not hosted an Olympics since the tragedy-marred Munich Games in 1972.
"We are convinced that it is a great opportunity for the city and for German sport in general," said DOSB president Alfons Hormann at a press
conference following the board meeting.
The board's decision also paves the way for a bid for the 2028 Summer Games in case they lose out in the 2024 race where an expected American bid will be the warm favourites.
However, even if as likely the general assembly rubber stamps the board's decision an obstacle will still remain as both Berlin and Hamburg will have to hold a referendum to see if their citizens wish to go forward with a bid.
Munich's hopes of once again bidding for the Winter Games - they came second to Korean candidate Pyeongchang for the 2018 edition - were dashed when residents voted against contesting the race for 2022 in a referendum in November 2013.
According to a poll carried out by the DOSB, 53 percent of Hamburgers are favourable to a bid compared to just 48 percent of Berliners.
Berlin has previously put a figure of €2.4 billion on hosting the Summer Games.
Berlin would spend €250 million on upgrading 15 existing sports facilities and €1 billion building temporary ones for the Games.
Under the capital's plan from outgoing mayor Klaus Wowereit, many of the events would be held in the surrounding states of Brandenburg, Mecklenburg-West Pomerania, Saxony-Anhalt, and Saxony.
Hamburg, meanwhile, plans to hold the majority of the events within a ten-kilometre radius of a new Olympic stadium. This central venue would be built on the island of Kleiner Grasbrook in the city's harbour on the Elbe River.
The name of the candidate city will be announced after the two referendums on March 21st next year and the DOSB will hand over the candidate's dossier to the International Olympic Committee (IOC) in November 2015.
The bid cities will learn whether they have won the right to host the 2024 Games after a vote by the 100-plus IOC members on September 17th 2017.