The 42-year-old has been handed the reins on a temporary basis, with Stimac counting the cost of Tuesday's 2-0 FIFA World Cup qualifying defeat away to Scotland.
Stimac offered his resignation in the immediate aftermath of the clash at Hampden Park, with Kovac appointed on the suggestion of Croatia Football Federation president Davor Suker.
Tuesday's disappointing loss to Scotland in the Group A fixture compounded a miserable week for Croatia, who also lost their crucial home encounter with Belgium on Friday and will have to settle for a play-off in order to reach Brazil 2014.
A first-half brace from Romelu Lukaku gave Marc Wilmots' side a commanding lead, and their automatic qualification hopes were curtailed despite Niko Kranjcar's late consolation.
