The Italian club publicly declared on Wednesday that a fee had been agreed between the clubs, but Tottenham have now confirmed that a deal for Lamela should be completed imminently.
The 21-year-old is widely expected to replace Gareth Bale in Tottenham's attacking line-up, with the Welsh winger reportedly on the verge of completing a €100 million move to Real Madrid.
Lamela becomes Tottenham's sixth signing of the transfer window following the acquisitions of Vlad Chiriches, Etienne Capoue, Roberto Soldado, Nacer Chadli and Paulinho.
The Argentine could now make his debut in Sunday's North London derby clash with Arsenal, with his arrival having been ratified by the Premier League in time for him to feature.
The former River Plate forward scored 15 goals in 33 Serie A appearances for Roma last season, helping the Italian club to a sixth-place finish.
Lamela has also been capped on two occasions by Argentina.
