The 22-year-old will join Spurs in the summer on a free transfer, the north London club announced on Friday, and his representative has stated that the Portuguese boss was the deciding factor in his destination.
"Schalke made Lewis a very good offer, we know that," Marcus Noack told Goal.com. "But this decision is not against Schalke.
"We had a lot of offers from every top league in Europe. If you look at the whole package, then Tottenham was the best choice.
"Andre Villas-Boas is especially convincing. This is a top coach. The decision to leave Schalke and join Tottenham came in mid-December. And it was very hard for us to choose."
Noack added that a transfer to Spurs in the January transfer window had not been discussed.
He continued: "The agreement says: [in the] summer. If a winter move was possible, I can't say right now, because we didn't talk about that."