It will be the first major international tournament staged in the country since the 2006 World Cup.
Germany are three-time European champions, having last triumphed at Euro 96.
Former Bayern Munich and Germany captain Philipp Lahm served as an ambassador for the bid, which will see games hosted in 10 cities.
Bayern's Allianz Arena, Borussia Dortmund's Westfalenstadion and Berlin's Olympiastadion are all included, while there will also be matches staged in Gelsenkirchen, Stuttgart, Hamburg, Dusseldorf, Cologne, Leipzig and Frankfurt.
The 2024 edition returns to the traditional arrangement of a single host nation, with Euro 2020 set to take place in 12 cities spread across the continent.