The 22-year-old had already agreed to join from Schalke at the end of his contract in the summer, before the north London side brought the transfer forward.
Spurs paid £1.5m to bring Holtby to White Hart Lane before the end of the January transfer window, and Villas-Boas hinted that the playmaker might make his debut on Wednesday.
“We rate the player very highly,” he said.
“We managed to get him at a good price, it was always a question of how much Schalke would want for the player.
“I think there was willingness from the player to come early so we have decided to add him to the squad – he is an extremely talented attacking midfielder who can play in a variety of roles.
“He is used to playing in different positions, he is young and talented – I think he is an excellent addition for us.
“He has been selected for the game (at Norwich) – he has just had one training session so we will decide wisely if it (playing) is appropriate or not.”
Holtby has scored 13 goals in 78 appearances for Schalke after joining from Alemannia Aachen in 2007.