The Allianz Arena - home of the mighty Bayern Munich and second division side 1860 Munich - trumped Berlin's Olympic Stadium, the German Football Federation (DFB) announced in Frankfurt on Friday.
DFB president Wolfgang Niersbach said: "It was not an easy decision to make because in Munich and Berlin we had two strong applicants who have shown on many occasions that they can manage large events.
"We are sure that Munich as a location has a very good chance with Uefa to get Euro 2020 games."
The 2020 Euro tournament will for the first time be staged in 13 cities across the continent rather than in one host country.
The DFB will apply for one of two packages of matches offered by European football's governing body Uefa, with September 12th the deadline for submissions.
The first option is to stage three group matches and a knockout match while the second is for the two semi-finals and the final.
Munich's mayor Christian Ude said the Bavarian capital would once again be a "welcoming host", if it was selected for games.
The city was seen as the favourite over Germany's capital from the start. Uefa will decide in September 2014 which cities host which matches.