Stimac, who played in England for Derby County in the late 1990s, was elected on Sunday at an extraordinary session of the FA general assembly
The meeting, which the current FA leadership deems illegal, was attended by just 25 of the 49 members that comprise the full assembly, but all voted for Stimac.
In December, Vlatko Markovic, was re-elected president by 25 votes to 24 but Stimac immediately denied the legality of the voting procedure.
He then succeeded in collecting enough signatures from members to request the weekend's meeting, disregarding the official leadership.
FA Secretary-General, Zorislav Srebric, told Reuters that, contrary to local media reports, there was no immediate threat of sanctions from UEFA or FIFA over the power struggle.
"At the moment, there is no risk of any sanctions. Moreover, we have received a written information from UEFA and FIFA that they recognise the leadership elected in December," Srebric said.
Stimac, 43, said neither UEFA nor FIFA had jurisdiction over internal matters of any football federation unless there was a direct involvement with politics.
Markovic was quoted by the Jutarnji List daily on Monday as saying that eventually UEFA could suspend the national team from further participation in the Euro 2012 qualifying campaign if the power struggle continued.
According to the FA statute, one third of representatives in the general assembly can seek an extraordinary meeting and Srebric said the FA had called such a meeting for April.
Stimac told the local media he would in the meantime try to secure formal registration of the newly elected FA leadership with the relevant authorities.
