The 44-year old Stimac succeeded former Hajduk Split team-mate Slaven Bilic, who stepped down after six years in charge following an early Euro 2012 exit and took over Russian first division side Lokomotiv Moscow.
Stimac, who partnered Bilic in the centre of Croatia's defence when they finished third in the 1998 World Cup, said he would raise the bar in order to bring the best out of his team.
"I believe we can look forward to better things and I will do everything in my power along with my staff to raise the level of our performances and results," Stimac told a news conference.
"We plan to improve things gradually and instil more confidence into the squad because we want to go to Brazil as contenders, not as also-rans.
"We are in the toughest of Europe's nine qualifying groups for the 2014 World Cup and it's also the most competitive qualifying group for a major tournament Croatia has ever been drawn in," he said.
The Croatians were pitted alongside neighbours and traditional rivals Serbia, Belgium, Scotland, Wales and fellow former Yugoslavs Macedonia.
Stimac was appointed after Thursday's inauguration of former Real Madrid striker Davor Suker as Croatia's FA (HNS) chief.
Suker, who won the 1998 Champions League with Real and then took the Golden Boot in that year's World Cup, said he would meet with Croatian President Ivo Josipovic in due course to discuss anti-hooliganism measures.
"We are ranked among the world's top 10 teams and as such highly valued abroad, but incidents such as those some of our fans caused in Euro 2012 are damaging our reputation," he said.
"We want to be a respected team in Brazil, not one that will keep paying fines for fan misbehaviour."
Croatian fans repeatedly caused trouble in Euro 2012 and the HNS was fined after some of them racially abused Italy striker Mario Balotelli and also displayed racist banners in their 1-0 defeat by eventual champions Spain.
