As revealed by Goal, the Serie A outfit accepted a €30 million (£25.7m) offer for the attacking midfielder, who has signed a five-year contract, on Monday.
|40/1||Tottenham are 40/1 with Bet365 to beat Arsenal 3-0
Roma confirmed the player's imminent sale on Wednesday, with the Argentine flying to England to complete a medical on Thursday, bolstering Andre Villas-Boas's squad ahead of the expected confirmation of Gareth Bale's world-record transfer to Real Madrid.
Lamela, whom Tottenham legend Ricky Villa told Goal will "improve dramatically" at White Hart Lane, becomes the club's second confirmed signing of Friday, with defender Vlad Chiriches having completed his move from Steaua Bucharest.
After Ajax technical director Marc Overmars confirmed talks, Spurs are also expected to finalise the transfer of midfielder Christian Eriksen.