The 6'5" centre-back moves to White Hart Lane in an €10 million deal, signing a four-year contract, and becomes Spurs' fifth signing of the summer after Michel Vorm, Ben Davies, Eric Dier and DeAndre Yedlin.
Mauricio Pochettino highlighted the defence as an area that needed reinforcement upon his arrival at the club and opted to sign Fazio after a deal for Villarreal's Mateo Musacchio stalled.
"I'm really happy to be here at this club, this great club with very good players. I’m really happy to be here," he told the club's official website.
"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's arrival follows the departure of Michael Dawson, with Hull City having completed the 30-year-old's signature on a three-year contract on Tuesday.
The 27-year-old moved to Sevilla in 2007 and has gone on to make over 200 appearances for the club, notably excelling last season as Los Rojiblancos won the Europa League.