Porro will join the Spurs on loan until the end of the season, with an obligation to make the deal permanent in the summer.
The Spain international was Spurs' top target this window, with talks with Sporting taking place for most of the month. He becomes their second signing in January after the arrival of winger Arnaut Danjuma on loan.
The 23-year-old Porro joined Sporting on loan from Manchester City in 2020, before signing permanently for the club in 2022.
He made 98 appearances for Sporting, the last of which came in a 2-0 Portuguese League Cup final defeat to Porto on Saturday when he was pictured afterwards waving to fans in an apparent farewell.
Spurs manager Antonio Conte has had his sights set on a new right wing-back, with Matt Doherty's contract with the club being mutually terminated on Tuesday in order that he could join Atletico Madrid.
Porro will now compete with Emerson Royal for the role.
Sporting earlier announced the signing of Hector Bellerin from Barcelona as a replacement for Porro.