The Italian side has affirmed that the Argentine forward has been sold to Tottenham as Spurs break their previous transfer record for the third time this summer.
The Italian club has also signed Adem Ljajic from Fiorentina to replace the forward.
Goal exclusively revealed on Aug. 14 that Spurs had entered into negotiations for the Argentine forward as a potential replacement for Real Madrid target Gareth Bale, while on August 20 Goal also learned that talks had escalated with Giallorossi officials in London.
The deal has now been confirmed by the Italian capital club after negotiations persisted for two weeks, the final stumbling block to its completion having been the fee.
Final arrangements see Lamela depart the Serie A giant for the sum of 30 million euros, with up to an additional 5 million euros available in the form of performance incentives.
Tottenham technical director Franco Baldini, who brought the 21-year-old to the Stadio Olimpico in the summer of 2011 from River Plate while a director at Roma, has now succeeded in breaking Spurs' previous record transfer figure for the third time in the present window after earlier brokering deals for Roberto Soldado and Paulinho.
Lamela, renowned for his dribbling and pace, tallied 15 goals and 5 assists in 33 Serie A appearances last campaign, while going as an unused substitute in Roma's season opening 2-0 win against Livorno on Sunday.
The move looks to have set the stage for Bale's protracted transfer to Real Madrid to be pushed through, Spurs having obtained the desired successor to the Welsh star.