The club sacked Markus Gisdol on Monday, appointing 61-year-old Bundesliga veteran Huub Stevens as his successor until the end of the campaign, with the Dutchman tasked with keeping struggling Hoffenheim up.
"We know this is a courageous step but we see in him (Nagelsmann) such a huge coaching talent that we want to give him a prospect," Hoffenheim sports director Alexander Rosen told a news conference at Stevens' presentation.
He said Nagelsmann had been given a three-year deal.
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Briefly an assistant coach during the 2012/13 campaign, Nagelsmann will remain with the Under-19 team until the end of the season as he continues studying for his senior coaching licence.
"I am looking forward to a very tempting task and I would like to thank everybody for the trust and the opportunity given to me," Nagelsmann, who coached Hoffenheim's junior team to the 2014 German title, said in a club statement.
Hoffenheim, backed by billionaire Dietmar Hopp, are in 17th place with one win and six points from their first 10 games of the season.
(Reporting by Karolos Grohmann; Editing by Ken Ferris)
