The 44-year-old Stimac, who made 53 appearances for Croatia as a defender, replaces Slaven Bilic who stepped down following UEFA EURO 2012 after six years at the helm. Croatia were knocked out of the UEFA European Championship at the group stage after finishing third behind the two teams who ended up reaching the final, Spain and Italy.
Croatia now turn their attention to the 2014 FIFA World Cup Brazil™, with their first qualifying match coming against Macedonia on 7 September. The other teams in Group A are Serbia, Belgium, Scotland and Wales.
Stimac said on uefa.com: "I am proud of what Slaven Bilic and the players did at Euro 2012, they left a great impression. In Brazil in two years there is a festival of football and Croatia will be there. I will do my best to make it happen."
Stimac, who represented Hajduk Split, Derby and West Ham as a player before becoming coach at Hajduk, Cibalia and most recently NK Zagreb, played alongside Bilic for Croatia during the 1990s.
Another member of that squad, Davor Suker, has been elected as the new president of the Croatian Football Federation (HNS).