The Germany U-21 international, whose father is from Liverpool, will move to White Hart Lane at the end of the season.
Holtby said: "When I was a lad, I used to sit with my dad in front of the TV and long to play there. 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 long ago."