News of the 27-year-old's arrival, for a reported fee of £8 million ($13.3 million, 10 million euros), comes a day after Tottenham allowed long-serving central defender Michael Dawson to join Hull City.
"We are delighted to announce that we have completed the transfer of Federico Fazio from Sevilla," Tottenham said in a statement on their website.
"The Argentina international has joined us on a four-year contract."
Fazio spent seven seasons at Sevilla and won the Copa del Rey, the UEFA Super Cup, the Spanish Super Cup and last season's Europa League during his time in Spain.
"I'm really happy to be here at this club, this great club with very good players," Fazio told Spurs' official Twitter account.
"I'm really happy to be here. I come to Tottenham because I think it's a very good team, a very good club, very good fans.
"I know Spurs is a historic club in this country and league. This is a great club and I'm very happy to be here."
Fazio began his career with Argentine side Ferro Carril Oeste and joined Sevilla in 2007.
He has won two Argentina caps and was a member of the squads that enjoyed success at the Under-20 World Cup in 2007 and the 2008 Beijing Olympics.
He is Spurs' fifth close-season signing after goalkeeper Michel Vorm and defenders Ben Davies, Eric Dier and DeAndre Yedlin.