The 22-year-old had initially been expected to join Spurs from Schalke 04 at the end of the season, but Andre Villas-Boas pushed through a move to acquire the German's services this month.
"I have been living my dream for the past few days. I am playing at an absolute top club in the Premier League. It has been overwhelming since arriving in the motherland of football," Holtby said in his blog.
The German has three international caps to his name.