Germany were selected by UEFA over a bid from Turkey to host Euro 2024, confirmed yesterday in Nyon by a 17-member UEFA Executive Committee.
Germany last hosted the event in 1988 - when the country was split in two - and have lifted the trophy three times. They also staged the World Cup in both 1974 and 2006.
Speaking to the German Football Association website, Löw said: "A tournament like this is exceptional for our country.
"It's a good step for the next few years, and everyone in the association can now plan ahead for it.
"Such a tournament can really motivate younger players as well.
Philipp Lahm also responded to the feat, remarking: "I feel great anticipation and am mightily relieved.
"We have excellent stadia, and fans who adore football.
"We're very welcoming and we want to show that.
"We've done a lot of preparation, and we want to share this and get everyone involved."