Croatian Tudor, who has managed several clubs across Europe, including Galatasaray and Olympique de Marseille, last led the Serie A giants Juve in Turin but now has Juventus.
"It is an honour to join this club at an important moment," Tudor said in a statement.
"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."
The 47-year-old guided Juve to a fourth-place finish in Serie A last season but he was sacked in October -- seven months after his appointment -- following an eight-match winless run in all competitions.
Tudor will have a baptism of fire when he takes charge of his first match against Premier League leaders and bitter rivals Arsenal in the North London derby on February 22.
Tottenham are ailing in 16th in the Premier League, with Spurs' sporting director Johan Lange saying: "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."
A former centre back who spent the majority of his career at Juventus, Tudor won back-to-back Serie A titles as a player between 2001 to 2003 and reached the 2003 Champions League final.
He began his managerial journey with Hajduk Split in 2013, while he is familiar with Spurs players Dejan Kulusevski and Rodrigo Bentancur, having been an assistant to Andrea Pirlo at Juventus in 2020-21 when they were at the Italian club.
The former Croatia international espouses an aggressive style of play built on pressing high up the pitch, with his teams also relying on quick transitions.
Spurs had appointed Frank prior to the season after his successful spell at Brentford but the Danish manager was unable to make the step up from successful mid-table management to a team which had just won the Europa League.
Apart from climbing up the standings, Tudor will also be charged with their progress in the Champions League where Spurs have qualified for the last 16.
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