Holtby, who had also been linked with Liverpool and Arsenal, will join Spurs on July 1, pending a successful medical examination.
The midfielder, 22, recently informed Schalke he would not consider signing a new contract and will now move to the country of his father's birth when his current deal expires.
Prior to confirmation of the transfer, Tottenham assistant manager Steffen Freund said Holtby would adapt quickly to life in the Premier League.
"For Lewis it will not be a problem," Freund said. "He is half-English, he loves the Premier League.
"He is captain of the Under-21s for Germany, he will lead the team at the European Championship in Israel."
Holtby, who has a German mother and was born in Erkelenz, signed for Schalke in the summer of 2009 and went on to enjoy loan spells at Bochum and Mainz prior to making his breakthrough at the Gelsenkirchen-based club.
Although he was eligible to play for England through his father, a former soldier in the British army who used to be stationed in Monchengladbach, Holtby opted to represent his country of birth.
He rose through the national youth team ranks before earning three full caps for Germany.
He is the current captain of the Germany Under-21 side and is expected to lead the team at this summer's European Championship in Israel.