Spurs confirmed Villas-Boas had signed a three-year contract. The club have also appointed two members of his coaching staff - fitness coach Jose Mario Rocha and opposition scout Daniel Sousa.
Villas-Boas said: “Tottenham Hotspur is a great club with a strong tradition and fantastic support, both at home and throughout the world. I feel privileged to be its coach. For me, this is one of the most exciting coaching positions in the Premier League.
"This is a squad any coach would love to work with and together I believe we can bring success in the seasons ahead."
Villas-Boas was sacked by Chelsea in March after a disappointing run of form in the Premier League that left the Blues in fifth place.
Chelsea had paid Villas-Boas's £13.3 million release clause to recruit him from Porto last summer but an attempt to overhaul Chelsea's team proved problematic.
Having been linked with a number of other jobs - notably Roma and Inter in Italy - Villas-Boas will now take the reins at White Hart Lane in an effort to rebuild his reputation in England.
Chairman Daniel Levy said: "He has an outstanding reputation for his technical knowledge of the game and for creating well-organised teams capable of playing football in an attractive and attacking style.
"Andre shares our long-term ambitions and ethos of developing players and nurturing young talent, and he will be able to do so now at a new world class training centre.”