Munich and Berlin wanted to host games at the tournament that will be staged by cities across the continent, with the DFB opting for the Bavarian capital, home of Champions League winners Bayern Munich.
"It was no easy decision because we had two strong bids with Berlin and Munich," said DFB president Wolfgang Niersbach in a statement. Berlin will host the 2015 Champions League final.
"We are convinced that Munich as a location has very good chances to get a package (of games) for the Euro 2020."
The finals will take place in 13 cities across Europe.
The DFB said it would apply for either of two packages of matches offered by European soccer's governing body UEFA by September 12.
The first package is to stage three group matches and a knockout round match and the second is for the two semi-finals and the final.
Munich has previously hosted several major events including the 1972 Summer Olympics, matches at the 1974 soccer World Cup - including the final - and in the 2006 World Cup.
The Bavarian capital failed with a bid to host the 2018 Winter Olympics.
(Reporting by Karolos Grohmann; Editing by Ken Ferris)
