The Portuguese former Chelsea, Real Madrid and Manchester United manager signed a contract until the end of the 2022/23 season, the north London club said in a statement.
Pochettino, 47, transformed Spurs' fortunes after arriving from Southampton in 2014 and although he failed to win a trophy he took the club to the Champions League final for the first time in their history just six months ago.
But the Argentine was sacked on Tuesday, with Tottenham struggling in the league after picking up just three wins from their opening 12 games.
This season they were knocked out of the League Cup by fourth-tier Colchester United and suffered an embarrassing 7-2 defeat at home to Bayern Munich in the Champions League.
One person who was definitely upset was Piers Morgan who joked: “Oh Jose, how could you do this to me?”
The vocal Arsenal fan also took a dig at the Spurs and said: “No wonder Spurs fans are furious about Mourinho - he's won 6 League titles in 3 countries, which is totally off-brand for those serial losers.”
- Exciting 'quality' - "I am excited to be joining a club with such a great heritage and such passionate supporters," said Mourinho, who has won domestic league titles in four different countries -- Portugal, England, Italy and Spain.
"The quality in both the squad and the academy excites me. 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. 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."
Mourinho has won Champions League titles with Porto and Inter Milan.
The 56-year-old Portuguese won three Premier League titles over two spells in charge of Chelsea and returned to England to manage Manchester United in 2016.
Mourinho was sacked last December following a poor run of results and has been out of work since, most recently working as a TV pundit.
His first match in charge will be the London derby away to West Ham on Saturday. Despite their recent poor run, Tottenham thrived under Pochettino's leadership.
They qualified for the Champions League four times, culminating in a dramatic run to the club's first ever European Cup final in June, which they lost 2-0 to Liverpool in Madrid.
However, domestic results had been on the decline since February, with Spurs clinging on to a top-four finish last season despite winning just three of their final 12 league games.
