In a vote delayed since November last year, the NFSBiH appointed a new 15-member executive committee and elected Elvedin Begic on a four-year term as its first president.
Since it was formed after the 1992-95 war and the country was divided into two ethnically divided regions, the federation has been run by a three-man presidency whose members were chosen on ethnic rather than professional grounds.
A Serb, a Croat and a Bosniak held the post for 18 months each under a rotational system, reflecting the country's general political system.
"Our first goal is to qualify for the (2014) World Cup and then for the (2016) European Championship," Begic told reporters. "Then we shall continue reforms of administration and of our local competitions."
Bosnia are trying to qualify for their first major international tournament as an independent nation and the election of a single president has removed the risk of further punishment from football's ruling bodies.
FIFA, which runs world football, and UEFA, its European counterpart, had told Bosnia to reform its presidential system and suspended the country from international competitions in April 2011.
The new executive committee elected on Thursday replaced an interim committee that was appointed by FIFA last year, allowing the lifting of its brief international ban.
Begic, an ethnic Muslim or Bosniak, was a deputy president of the interim committee. His two new deputies represent the Serb and Croat ethnic groups.