Blackpool have signed Derby striker Kwame Thomas on a six-month loan.
Norwich City have secured the services of Liverpool defender Andre Wisdom in a season-long loan deal.
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 centre-half 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."
Sky sources, meanwhile, understand Sevilla are interested in replacing their captain with Celtic centre-half Virgil van Dijk.
Celtic are reluctant to sell the 23-year-old, who is also the subject of interest from two Premier League clubs.