Udogie, 19, has signed to a five-year deal, and add-ons may increase the price to an additional £3 million.
The Under-21 international from Italy, who just recently made a permanent move to Udinese this summer, will be loaned back to them for the remainder of the season.
He was a left-back who played 35 league games for Udinese last season, recording five goals and four assists.
Udogie joined Udinese on a season-long loan from Hellas Verona in July 2021, and as part of that agreement, they were required to purchase him this summer. By that point, his performances had piqued the curiosity of rival teams.
Following the additions of Ivan Perisic, Richarlison, Fraser Forster, Yves Bissouma, Clement Lenglet, and Djed Spence, Udogie is Tottenham’s sixth summer acquisition.