Germany parted ways with Flick earlier this month, a day after their 4-1 home loss to Japan in a friendly match, with the four-time world champions struggling for form in recent years.
Julian Nagelsmann spoke of his appointment, explaining: "We have a European Championship in our own country. That's something special - something that happens every few decades.
"The target is next summer and the Euros, that is a great challenge for me," he told a press conference.
"We take it on with a lot of responsibility. A whole nation behind us and we want to excite them with great football."
"We want to play football with a specific idea. But we also demand attractive football, not just based on results," he added. "A Euro at home with the whole nation behind you. That's is our aim."
DFB President Bernd Neuendorf added in a statement: "Next year's European Championship is of enormous importance for football in Germany as a whole. We are convinced that Julian Nagelsmann, as national coach, will ensure that the national team inspires its fans and that the EURO is also a sporting success.
"Julian Nagelsmann is an outstanding coach who approaches his new task with the highest level of motivation.
"We will all now focus on the tournament next summer and support Julian Nagelsmann as best we can."
Nagelsmann has had a swift rise to the pinnacle of German football. He started management at the age of 28 with Hoffenheim and since then has managed RB Leipzig and Bayern Munich.
Germany's current assistant Sandro Wagner will continue to support Nagelsmann as an assistant in the future, and Benjamin Gluck will be the other assistant coach of the national team.
Flick, assistant coach to his predecessor Joachim Low when Germany won the World Cup in 2014, took over in 2021, but his team managed four wins in their last 17 internationals and were also eliminated in the group stage of the World Cup last year.
It was their second consecutive first round World Cup exit.
With the Euros on home soil in less than nine months, the four-time world and three-time European champions are desperate to forge a battle-ready team in time for the tournament, the first major international football competition in the country since the 2006 World Cup.