The 22-year-old has walked away from Champions League football to join the Premier League's fourth-placed side, but insisted it was an easy decision to make.
He told Tottenham's official website: "It is fantastic to be here. I can't wait to settle and to play for the club and I am looking forward to the season.
"The facilities are the best I have seen. I am proud to be here, a huge club that is only getting bigger and bigger.
"I played Champions League with Schalke, but I wanted to be here now.
"As soon as I saw the facilities, the crowd and spoke to Andre, I just knew I wanted to be here. I am over the moon."