The winger will join Spurs in a club-record deal rising to a possible £30 million, with Adem Ljajic arriving at the Serie A outfit from Fiorentina as his replacement
Goal exclusively revealed on August 14 that Spurs had entered into negotiations for the Argentine forward as a potential replacement for Real Madrid target Gareth Bale, before confirming talks had escalated with Giallorossi officials in London.
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"AS Roma gives notice that it has agreed a deal with Tottenham Hotspur for the outright sale of Erik Lamela for a fee of €30m," a club statement read.
"The agreement contains the recognition of a corresponding variable fee, up to a maximum of €5m, for bonuses linked to the player's achievements of certain sporting objectives."
Andre Villas-Boas revealed on Wednesday that Bale's move to the Santiago Bernabeu was imminent, with news expected "very soon".
Real Madrid set up a stage inside their stadium ahead of an expected presentation, with the two clubs agreeing a world-record £86m deal for the Welshman.
The £30m deal signals the third time Tottenham have broken their transfer record this summer following the arrivals of Paulinho, for £17m, and Roberto Soldado, for £26m.
The 21-year-old enjoyed an excellent season with the Italian capital club last season, scoring 15 goals in 36 appearances as Roma finished sixth in Serie A, though they were beaten in the Coppa Italia final by rivals Lazio.