Former Chelsea and Manchester United boss Mourinho has signed a contract until the end of the 2022-23 season.
"The quality in both the squad and the academy excites me," said the 56-year-old Portuguese. "Working with these players is what has attracted me."
Spurs chairman Daniel Levy said: "In Jose we have one of the most successful managers in football."
Tottenham reached the Champions League final last season under Pochettino but lost to Liverpool in Madrid.
The Argentine, who was appointed in May 2014, failed to win a trophy in his time in charge of the north London club with Spurs' last silverware being the League Cup in 2008.
Levy added: "He (Mourinho) 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."
Mourinho still lives in London and won three Premier League titles and one FA Cup in two spells at Chelsea, while he won the Europa League and Carabao Cup with Manchester United.
He has also previously managed Portuguese side Porto - where he won the Champions League - Italian club Inter Milan, with whom he claimed a league, cup and Champions League Treble, and Spanish team Real Madrid, who he led to the La Liga title.
Mourinho has been out of work since being sacked as Manchester United manager in December 2018.
He takes over a Spurs side that are 14th in the Premier League and without a win in their last five games.
Mourinho has turned down a number of job opportunities, including in China, Spain and Portugal, since leaving Old Trafford.