The 32-year-old is seen as one of the best young managers in Europe and was said to be on Spurs' shortlist to replace the axed Mauricio Pochettino at Tottenham until they landed José Mourinho.
Nagelsmann has led his Leipzig side to back-to-back top-four finishes and this term shows no sign of being any less of a success, as they sit two points clear at the top of the Bundesliga table, with reigning champions Bayern Munich in second.
The first leg will be in London at Tottenham's brand-new billion pound stadium in north London and Nagelsmann is "looking forward" to the challenge.
"Tottenham is a very nice and exciting tie!" he told Leipzig's Twitter account. "They're one of Europe's top teams, playing in a fantastic city with star players who have a lot of experience. It won't be easy but we're really looking forward to it, especially playing in that stadium".