The former Chelsea and Manchester United boss has signed three-and-a-half-year contract with the London club.
The appointment comes less than 12 hours after Spurs parted company with Pochettino on Tuesday evening.
The 56-year-old Portuguese said: "I am excited to be joining a club with such a great heritage and such passionate supporters.
"The quality in both the squad and the academy excites me. Working with these players is what has attracted me."
Mourinho, who won three Premier League titles in two spells with Chelsea, had been out of management since leaving United in December last year.
Spurs chairman Daniel Levy said: "In Jose we have one of the most successful managers in football.
"He has a wealth of experience, can inspire teams and is a great tactician. He has won honours at every club he has coached. We believe he will bring energy and belief to the dressing room."
A statement from the club added: "Jose is one of the world's most accomplished managers having won 25 senior trophies.
"He is renowned for his tactical prowess and has managed FC Porto, Inter Milan, Chelsea, Real Madrid and Manchester United.
"He has won a domestic title in a record four different countries (Portugal, England, Italy and Spain) and is one of only three managers to have won the UEFA Champions League twice with two clubs, FC Porto in 2004 and Inter Milan in 2010."
Pochettino was dismissed after five-and-a-half years in charge, less than six months after he took Spurs to the Champions League final, with the club lying 14th in the Premier League table after the opening 12 matches.
Mourinho, who has most recently been working as a pundit for Sky Sports, had turned down a number of opportunities to coach abroad since leaving United, including with clubs in China, Spain and Portugal.
His first match in charge will be the London derby away to West Ham on Saturday and they are due to play United at Old Trafford on December 4.
Spurs also play Champions League games at home to Olympiakos and away at Bayern Munich before hosting their new manager's former club Chelsea on December 22.
Mourinho's side host Liverpool on January 11 and Manchester City on February 1 before making the trip to Stamford Bridge on February 22.