Tudor, who had two spells in the side as a player, has taken over at Hajduk following Mise Krsticevic's decision to part company with the club on Monday.
Krsticevic left after Sunday's 2-1 home defeat by HNK Rijeka, which resulted in the visitors overtaking the hosts in third place in the league table.
The role will be Tudor's first as a head coach and the 35-year-old is excited about the opportunity, particularly because it's at a club he holds so dear to his heart.
"This is great for me, to get an opportunity at the beginning of my coaching career and to work in the city where I was born and the club where I grew up," Tudor told UEFA.com.
"My goal will be to get the maximum out of the players and we will try to book a European place. I am confident I can do a good job."
Tudor made 55 appearances for Croatia between 1997 and 2006, scoring three goals in the process. The peak of his club career was spent at Juventus between 1999 and 2007.
Hadjuk face NK Lokomotiva in the two-legged Croatian cup final later this month.