The former Manchester United and Chelsea boss replaces Mauricio Pochettino, who was sacked on Tuesday.
His first game will be at the London Stadium on Saturday as Spurs travel to take on West Ham in the Premier League.
Pochettino left Tottenham with the club 14th in the Premier League and having won just five matches all season.
Chairman Daniel Levy said he was “reluctant” to sack the Argentine, but explained the decision had to be made in the “club’s best interests”.
“If Jose wants to get into top-level management, you’ve only got to look at his CV,” he told Sky Sports News. “People question the Manchester United job, but his career as a whole has been hugely successful, and that’s one thing Tottenham have lacked at the moment.
“As well as Pochettino has done, they haven’t quite got over the line to get a trophy, and that’s what Jose Mourinho does when he goes to a club.”
“Is he the right fit for Tottenham? It’s interesting, as Jose likes to spend money, and Daniel doesn’t, and Jose would want to get some really big names into the building,” explained Redknapp.
“He likes experience, and isn’t really one for playing young players, but you can’t argue with what he’s done in the game.”