Tudor has signed to the end of the season and steps up after the dismissal of Thomas Frank this week.
The Croatian was available after being axed by Juventus earlier this season.
Tudor said: “It is an honour to join this Club at an important moment.
“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.”
On the appointment, Sporting Director Johan Lange said: “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.”