The decision -- which saw Hamburg gain 18 votes to Berlin's 11 with four voters voting for both cities -- should be rubber-stamped by a DSOB Extraordinary General Assembly meeting in Frankfurt this Saturday and a referendum will be held in the winning city to ensure the local population are behind a bid.
Both cities stated their case in a 15-minute presentation during the day-long meeting with 43 representatives from sports, politics and civil societies in Frankfurt.
"How close the two cities were together is clear from the voting," said DSOB president Alfons Hoermann.
"Hamburg offers a fascinating and compact concept and the development of a north German and north European metropolitan region can be promoted."
Hoermann continued: "We are looking forward to the presentation on Saturday, then the work will really begin.
"We want to stay in constant dialogue with the citizens and the public.
"Only then will it be possible for the vision of an Olympic and Paralympic Games to become a reality in Germany."
The DSOB are still mindful of Munich's proposed bid for the 2022 Winter Olympics which had to be dropped after organisers in Bavaria lost a local referendum.
An opinion poll published last week showed 64 percent of Hamburg residents approve their city hosting the Olympics, compared to 55 percent in Berlin, whose unsuccessful bid for the 2000 Games was undermined by protests.
Cities have until September 15 to formally enter the race and so far Boston and Rome have officially declared, although Paris is also expected to announce a bid.
The International Olympic Committee (IOC) are due to choose the host city in 2017.