Spurs said the 19-year-old, reportedly a target for Paris St Germain, had signed a five-year deal.
Last week they signed Colombia central defender Davinson Sanchez from Ajax Amsterdam for a club record fee reported to be about 42 million pounds, and they have also brought in goalkeeper Paulo Gazzaniga from Southampton.
No tansfer fee was disclosed by Tottenham for Foyth, who represented Argentina at the 2017 Under-20 World Cup, but local media said it was eight million pounds ($10.33 million).
"This club believes in young players and I'm very happy to be here," Foyth told Spurs' website (www.tottenhamhotspur.com). "I think there's a wonderful project here."
Tottenham boasted the best defence in the league last season but have sold England right back Kyle Walker to Manchester City and Austrian stand-in centre back Kevin Wimmer to Stoke City.
The north London club are reportedly close to confirming the signing of PSG's right back Serge Aurier.
Spurs, runners-up to Chelsea last season, have suffered a disappointing start to the current campaign, picking up four points from the opening three matches.
(Reporting by Martyn Herman; editing by Ken Ferris)
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