The 34-year-old flew into London on Monday for contract talks and agreed terms to become Harry Redknapp's successor at White Hart Lane.
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.
He will have been encouraged by the news that Gareth Bale has extended his contract at White Hart Lane but key midfielder Luka Modric is expected to leave the club.
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.”