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 Schalke.
Having announced last month he would not be extending his contract with the Bundesliga club beyond the end of the season, Spurs soon gave him his long-desired route into the Barclays Premier League with north London rivals Arsenal also interested in the player.
"When I was a lad, I used to sit with my dad in front of the TV and long to play there (in England)," Holtby wrote on his Facebook page.
"This chance has now arrived, and I have taken it. I have always said that it would be realising a dream for me to play in the Premier League one day. As soon as this became reality, it was a childhood dream come true."
Holtby took time out from Schalke's training camp in Doha to address the club's fans, many of whom have not taken too kindly to his decision to leave the Gelsenkirchen club.
"I hope that you can understand me and that we can enjoy the remaining games together," he added.
"Then I will look back on a great experience and time, and I am grateful to have been given this chance here in Schalke.
"I have always identified myself with this club and I will continue to do so until the very last second.
"If it weren't for my English roots and for the Premier League, then I would have signed a new deal (with Schalke) long ago."