Tudor, a former Croatia international, joins Spurs on a deal until June following Wednesday's dismissal of Thomas Frank.
The 47-year-old's first game in the dugout will be the north London derby against Arsenal next Sunday.
"It is an honour to join this club at an important moment," Tudor told Tottenham's official website.
"I understand the responsibility I have been handed and my focus is clear. To bring greater consistency to our performances and compete with conviction in every match.
"There is strong quality in this playing squad, and my job is to organise it, energise it and improve our results quickly."
Tudor takes over a Tottenham side 16th in the Premier League, five points above the relegation zone and winless in eight league games.
Frank was axed after just eight months in charge, with his final match a 2-1 defeat at home to Newcastle.
The Dane had more success in the Champions League, though, guiding Spurs into the last 16 automatically with a fourth-place finish in the league phase.
Tottenham sporting director Johan Lange said of Tudor: "Igor brings clarity, intensity and experience of stepping into challenging moments and producing impact.
"Our objective is straightforward – to stabilise performances, maximise the quality within the squad and compete strongly in the Premier League and Champions League."
Tudor has been out of work since October after being sacked by Juventus following a seven-month spell in Turin.
He was dismissed with the club eighth in Serie A and in an eight-game winless run.
Tudor won Serie A twice in nine years as a player with Juve before heading into management with Croatia's Hajduk Split in 2013.
He has managed various clubs since then, having stints at the likes of Galatasaray, Udinese, Marseille and Lazio.