The 35-year-old, who was Slaven Bilic's assistant during his stint in charge of the Croatian national side, has more recently been coaching Split's youth teams.
"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's official website.
"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 started and ended his career with Split, having also spent eight years with Juve.