The Argentine has signed a four-year deal after Spurs agreed to meet a reported £8m buyout clause in his Sevilla contract. Fazio's arrival comes after the collapse of an earlier move for Villarreal's Mateo Musacchio, and 24 hours after centerback Michael Dawson left White Hart Lane for Hull.
Shortly after Spurs announced the deal Fazio tweeted: "I'm really happy to be here at this club, this great club with very good players. 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."
Meanwhile, Tottenham boss Mauricio Pochettino insists that Roberto Soldado and Andros Townsend remain in his plans and will not be sold during the current transfer window. Neither player has started either of Spurs' two Premier League games this season, leading to reports that they may be sold before Monday's deadline.
AC Milan have been linked with Spanish striker Soldado, who has struggled to justify the Â£26m Tottenham paid to sign him from Sevilla last summer, but did score one of the north London club's goals in the 2-1 Europa League qualifying first leg win at AEL Limassol.
But Pochettino, who left Southampton to take over at Tottenham this summer, said: "Soldado is here. I never talk about any player rumors. He is in my plans. For the future? Yes. Yes. We've only had two games in the Premier League and one in the Europa League. I believe in all the squad. It is important you know I can only pick 11."
England international Townsend, who also started the European tie in Cyprus, saw his first-team opportunities limited by injury last season and has been linked with a move to QPR. "He is in my plans," Pochettino said of Townsend. "It is impossible you play or have in the squad only 11 players - you need 24 or 25 players.
Sky Sports sources, meanwhile, understand Sevilla are interested in replacing their captain with Celtic's Virgil van Dijk. Celtic are reluctant to sell the 23-year-old, who is also the subject of interest from two Premier League clubs.