Following Slaven Bilic’s departure as coach, the Croatian Federation (HNS) has acted quickly to replace the ex-Everton defender who, like Bilic, also played for West Ham and the Croatia side which reached the semi-finals of the 1998 World Cup.
"I am proud of what Slaven Bilic and the players did at Euro 2012, they left a great impression," Stimac, 44, told UEFA’s website. "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."
Former Hajduk Split and NK Zagreb coach Stimac’s first competitive match in charge will be a World Cup 2014 qualifier against Balkan neighbours Macedonia on September, although there is a friendly with Switzerland on August 15.
Croatia are in a qualification group that also contains rivals Serbia, plus Belgium, Wales and Scotland.
Before Euro 2012, the 43-year-old Bilic had announced he would leave Croatia after six years in charge. He is now Lokomotiv Moscow coach.
Croatia failed to reach the knockout stages of the Euros, although they were in a group that boasted the two eventual finalists Spain and Italy.
Stimac’s appointment comes as part of a full-scale overhaul at the HNS, with Croatia striking legend Suker - another ex-Hammers player and 1998 World Cup star - taking charge of the organisation after a unanimous board vote.
Former Real Madrid and Sevilla forward Suker replaces Vlatko Markovic, who had spent 14 years at the helm before being replaced by Sports Minister Zeljko Jovanovic in December after a series of match-fixing, refereeing, financial and hooligan crises rocked the domestic game.
Croatia were also fined three times during the Euros for racist behaviour by fans during group games against Ireland, Spain and Italy.
Suker declared his intent to clean up the Croatian game, saying that the clubs needed to play a role to “settle accounts with individuals and groups that harm Croatian football."
Since retiring from football Suker has run a football academy in Zagreb.