Italian media reported that Tudor has signed an 18-month contract with the Rome club.
Tudor last coached French side Marseille, leaving in June last year after leading them to a third-place finish. He has also managed Serie A teams Udinese and Verona. The Croatia international played in Serie A as a defensive midfielder for Juventus from 1998 to 2007.
Sarri resigned on March 13th and Lazio assistant coach Giovanni Martusciello took charge for Saturday's 3-2 win at Frosinone.
Lazio are ninth in the standings, four points outside the European qualifying places.