The 20-year-old was born in England but moved to Portugal with his family as a six-year-old.
He joined Sporting's youth set-up at the age of eight and progressed all the way to the club's first team, making 30 appearances.
"I'm really excited to be joining such a big club," Dier, who spent a season on loan with Everton as a 17-year-old without making a first-team appearance, told the club's official website.
"It's always been my ambition to come back to England and play in the Premier League.
"I'm really happy to be here. I want to impress the manager and keep the fans happy, I just want to do as well as we can with the club.
"Spurs are a massive club. I've always enjoyed their attacking football and I think coming from Portugal that suits me - this season I want to adapt really quickly to the Premier League and have as good a season as we can."
Dier has already played with several Spurs players, including Andros Townsend, Harry Kane, Tom Carroll and Ezekiel Fryers with the England U21 and other age-group teams.
He has represented England at U18, U19, U20 and U21 level.