The 22-year-old had already agreed to move to White Hart Lane from Schalke in the summer at the end of his contract, but a £1.5m deal was struck to bring the move forward and the Germany international could make his debut as early as Wednesday night when Tottenham visit Norwich.
Holtby has walked away from Champions League football to join the Premier League's fourth-placed side, but insisted it was an easy decision to make.
He told Tottenham's official website: "It is fantastic to be here. I can't wait to settle and to play for the club and I am looking forward to the season.
"The facilities are the best I have seen. I am proud to be here, a huge club that is only getting bigger and bigger.
"I played Champions League with Schalke, but I wanted to be here now.
"As soon as I saw the facilities, the crowd and spoke to Andre, I just knew I wanted to be here. I am over the moon."
Villas-Boas is confident Holtby can make an instant impact for his team as they look to secure Champions League football for next season.
"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."
Meanwhile, Villas-Boas has quashed rumours that Jermain Defoe requires surgery on a recent injury.
There were reports that Defoe would need an operation after sitting out the FA Cup defeat to Leeds United, but Villas-Boas stressed he will not be making a move for a new forward in the window.
When asked if Defoe required an operation he said: "No, it is not true. It is extremely important [that Defoe can continue to play].
"We have spoken openly about this situation and we know it is a situation of risk and limit, but we are happy to take that risk at the moment. We are fine as we stand - it is something we are not considering."