No fee was disclosed but media reports say Spurs paid around four million pounds ($6.73 million)for the England under-21 International.
"It has always been my ambition and my dream to come back to England and play in the Premier League," the 20-year-old told the club website (www.tottenhamhotspur.com).
"I've watched a lot of Tottenham Hotspur and I've always enjoyed the way they play, their attacking football."
"I think, coming from Portugal, that suits me and this season I just want to adapt really quickly to the Premier League and do the best I can."
Dier's family moved to Portugal when he was a child.
He made 30 appearances for the Lisbon club, and spent time on loan at Everton in 2011.
He is Spurs manager Mauricio Pochettino's third signing following the arrival of Wales defender Ben Davies and Netherlands goalkeeper Michel Vorm, both from Swansea City.
Spurs open their league campaign at West Ham United on Aug. 16.
($1 = 0.5946 British Pounds)