The 22-year-old midfielder, whose father Chris is from Liverpool, will move to White Hart Lane at the end of the season when his contract expires with the German club.
A Spurs statement read: "We are delighted to announce that we have reached agreement with Germany Under-21 captain Lewis Holtby to join the club in July from Bundesliga side Schalke, subject to a medical."
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.
Tottenham's bitter rivals Arsenal were among a number of clubs interested in signing the player, but he sees his future at White Hart Lane.
Tottenham assistant manager Steffen Freund previously spoke highly of Holtby's potential.
Although Freund has not worked directly with Holtby, he is aware of the player's talents from his time coaching Germany's Under-16 and Under-17 sides.
"For Lewis it will not be a problem (adapting to English football)," 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.
"I worked for Under-16s and Under-17s for the last three years, that is why I don't know him really well but what I can say is that he is a really good player."
Holtby becomes Tottenham's second signing of the 2013 after the London club confirmed that they had bought promising teenage defender Zeki Fryers from Standard Liege.
It is understood Holtby has signed a four-year contract at Spurs that will expire in June 2017.