The former Borussia Dortmund and Liverpool boss was the DFB's immediate first choice to succeed Julian Nagelsmann, who resigned following the World Cup last-32 exit to Paraguay in June.
Klopp has been global head of soccer at the sports arm of drinks maker Red Bull, but will now lead Germany into the Nations League, qualifying for Euro 2028 in the British Isles and qualifiers for the 2030 World Cup. His contract will begin on August 15.
"It is a big honour to sit here," Klopp said on Friday.
"I had an idea how big the job is, but when you are involved you feel the responsibility even more. It is a very special day for me."
His first match in charge will be against the Netherlands in Amsterdam on September 24 in Germany's opening Nations League fixture.
Klopp is well-known for his charisma, but his press conference was not as joyful or comedic as some fans might have expected.
"On the day you don't want me anymore, tell me and I'm gone," he said, before appearing to warn the gathered media, "If you misbehave and don't leave my family alone, I'm gone."
The 59-year-old won two Bundesliga titles with Dortmund in 2011 and 2012, before lifting the Champions League with Liverpool in 2019 and the Premier League a year afterwards.
He left Liverpool in May 2024 to have a break from coaching, but said during talks with the DFB that his batteries were now "recharged."
Klopp, recently back in Germany after working as a MagentaTV World Cup pundit, said Red Bull had agreed a "generous" deal to let him leave a job where he had oversight over Red Bull's teams across the world, including RB Leizpig and New York Red Bulls.
Klopp is the 13th head coach of the Germany men's team. They have not won a knock-out game at a men's World Cup since winning the title in 2014.
Just before his press conference, a meeting of the DFB's supervisory board and wider stakeholders voted in a digital meeting to appoint Klopp.
His long-serving assistants Peter Krawietz and Pepijn Lijnders and his former Dortmund player Sven Bender were also approved by the DFB as assistant coaches.
Germany's 2014 World Cup winner Per Mertesacker, who spent eight years running Arsenal's youth academy, is also becoming the DFB's managing director for sport from January.
Amid talk that Germany no longer have a top world-class player, Klopp added: "As a coaching team we want to produce a package. We have a few weeks before the first match. It is enough time for me to prepare. We are all ready."
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