Kovac was promoted to his new position after excelling with the under-21 side, notching four wins out of four as the team scored 13 goals and conceded none in their Euro 2015 qualifying group.
"The HNS executive board decided unanimously to relieve Stimac of his duties and terminate his contract while the body has also decided to name Kovac as his successor," Suker told a news conference.
"It was a difficult decision because Stimac is a personal friend and a former Croatia team mate but a string of poor results and performances made it inevitable.
"Kovac will take over as the caretaker coach for the upcoming playoff but our intention is to offer him a long-term contract whether or not we reach the World Cup finals in Brazil."
Stimac, who took over from the more popular Slaven Bilic in July 2012, had an uneasy relationship with the media and fans from the start but seemed on course to win their hearts after a 2-0 home win over bitter Balkan rivals Serbia underlined Croatia's good start in Group A.
After that victory and a fortuitous 2-1 away defeat of Wales, the Croatians were joint top with Belgium on 16 points from five games but it all went wrong for Stimac and his men after a 1-0 home loss to Scotland.
Belgium ran away as group winners and won an automatic berth in next year's finals while Croatia held on to the runners-up spot with a 1-1 draw at Serbia, followed by a 2-1 home defeat by the Belgians and the turgid display in Glasgow.
"I am aware that Stimac offered his resignation in a statement to the media after the game but we received nothing from him in written or verbal form on the flight back or afterwards, hence he was sacked," said former striker Suker, who reached the 1998 World Cup semis with Croatia.
"Kovac is full of enthusiasm and we are hoping that he will steer us to Brazil because he is the right man for the hard work that lies ahead in a very short time frame."
Croatia reached the European qualifying playoffs as one of the eight best runners-up from nine groups, alongside France, Portugal, Sweden, Greece, Ukraine, Romania and Iceland.