Hmoud, who had served as deputy head of the association for seven years, has taken over as president following this week's resignation of Hussain Saeed.
"As much as I am happy about this for myself, I am also happy because this election puts an end to a long argument (and)puts an end to this era," Hmoud told Reuters.
"Iraqi football has witnessed deterioration in recent years. We will work hard to restore the success of Iraqi football."
Saeed, formerly one of Iraq's best-known footballers who also served as national coach, said in a letter he had quit in a bid to help free the sport of political and sectarian influence.
In August, world football's governing body FIFA gave the IFA a year to settle a bitter row which had blocked the leadership elections and put the Iraq team at risk of being suspended again from international competition.
The government of Shi'ite Prime Minister Nuri al-Maliki has been trying to remove top officials from sporting organisations suspected of having ties to the Sunni-led government of former dictator Saddam Hussein, who was hanged in 2006.
Saeed was a member of the Olympic Committee controlled by Saddam's son Uday.
Saeed had accused al-Maliki's government of interfering with the IFA elections and last year asked FIFA to allow a postponement.
The IFA twice failed to elect a president in July.
Hmoud, who served as national coach in 1999 and 2000, won the election over the government's choice, former player Falah Hassan.
FIFA rules require governments to refrain from meddling in national soccer federations and has suspended Iraq twice, lifting the latest ban in March 2010 on condition the federation agreed on a road map for new elections.
The row highlighted sectarian divisions more than eight years after the 2003 U.S.-led invasion that toppled Saddam.
Iraq captured the world's imagination by winning the Asian Cup in 2007 but have struggled since then and have employed a succession of coaches.
The country failed to qualify for the 2010 World Cup.
