Frank was dismissed after a run of just two wins in 17 Premier League games, with the club currently 16th and five points above the relegation zone.
Tudor's immediate task is to steer Tottenham away from the Premier League relegation zone.
The 47-year-old previously managed Juventus, where he led them to a fourth-place Serie A finish before being sacked in October after an eight-game winless run.
Tottenham's next fixture is against Arsenal on 22 February, with Mauricio Pochettino, Marco Rose, and Edin Terzic among the candidates for the permanent managerial role in the summer.
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