0645 GMT January 27, 2020
The Portuguese former Chelsea, Inter Milan, 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, according to AFP.
"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."
Argentine Pochettino was sacked on Tuesday, with Tottenham struggling in the league after picking up just three wins from its opening 12 games.
The 47-year-old had 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 its history just six months ago.
This season Spurs 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.
‘Energy and belief’
Mourinho, never shy of speaking his mind, famously said "I am a Special One" when he first arrived in the Premier League to manage Chelsea in 2004.
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 honors at every club he has coached. We believe he will bring energy and belief to the dressing room."
Mourinho won Champions League titles at home with Porto and then in Italy with Inter Milan.
The 56-year-old also won three Premier League titles over two spells in charge of Chelsea, and returned to England to manage Manchester United in 2016.
He was sacked last December following a poor run and has been without a club since, most recently working as a TV pundit.
His first match in charge will be the London derby at West Ham on Saturday.
Former Tottenham captain Gary Mabbutt told the BBC that Spurs were forced to act after a poor run.
"I think everyone at the club will always have great affection for Mauricio, but as a board of directors you have to look at the way things are going and the board had to make a decision."
Despite Spurs’ recent bad results, 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.
That form has continued at the start of this season and Mourinho arrives with the club 11 points outside the Premier League top four, 20 behind leader Liverpool and just six points above the relegation zone, though the club is well-placed to reach the last 16 of the Champions League despite the Bayern humiliation.
Levy said the club had been "extremely reluctant" to make the change, pointing at the poor domestic results.
The job done by Pochettino was all the more remarkable given the tight budget he was afforded by Levy for transfers and wages in comparison with Tottenham's Premier League rivals, as the club built a new stadium at a cost of more than £1 billion ($1.3 billion).
Instead, much of Pochettino's success came from nurturing a squad of young players into household names such as Harry Kane, Dele Alli and Christian Eriksen.
Spurs and England forward Harry Kane paid a warm tribute to Pochettino.
"Gaffer. I'll be forever thankful to you for helping me achieve my dreams," the England captain tweeted.
The Tottenham Hotspur Supporters' Trust questioned Levy's role in the diminishing results on the pitch.
"Is the manager solely accountable? How much has the board's line on wages and transfers contributed to player unrest and disaffection?" THST said in a statement.