The 21-year-old is set to move to Spurs in a deal worth €30 million (£25.7m), plus €5m (£4.3m) in performance-related bonuses, after the north Londoners agreed a deal with the Serie A side.
However, although Lamela is excited for the future at White Hart Lane, he admits that there was "something missing" during his time at the Giallorossi.
Tottenham are 13/8 with Coral to finish in the top four
"It’s also true that there was something missing for the whole team.
“I hope this season will go better. I saw the lads are hungry to do well and are very concentrated. I wish the club, the coach and my team-mates to go as far as possible."
Lamela started his career with River Plate before making the move to Serie A in 2011. He has subsequently made 66 appearances in his two seasons with Roma, scoring 21 times.
'El Coco' has also won three caps for Argentina and has not ruled out a return to Roma in the future.
“I am proud to have played for Roma and hope one day to return," he added.
“As for myself, now I hope to do well with Tottenham in London. I am ready. I want to thank and salute the fans who always behaved well with me. I embrace them all. They will always be in my heart.”Meanwhile, Roma completed the €11m (£9.4m) signing of Fiorentina's Adem Ljajic, who will serve as Lamela's replacement.