“In Jose we have one of the most successful managers in football,” said Spurs chairman Daniel Levy. “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 was sacked by United last December following a poor run and has been without a club since, most recently working as a TV pundit.
Despite his troubles in the latter stages of his tenure at Old Trafford, he remains a big name but is a divisive figure and there will be questions over whether his pragmatic style can mesh with Tottenham’s tradition of attacking football.
Pochettino had transformed the club’s fortunes since arriving in 2014, qualifying for the Champions League four times.
Although he failed to win a trophy, the club made a dramatic run to the European Cup final for the first time in their history in June, which they lost 2-0 to Liverpool in Madrid.
But that masked a worrying dip in domestic form in the second half of last season and Pochettino was unable to reverse the slide in this campaign.
They were also bundled 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.