Nashat Maher, the former head of military sports, was abducted on Saturday by dozens of gunmen dressed in military uniforms along with eight other committee members, a bodyguard and 20 security guards.
"He was found lying by the side of the road, blindfolded, in an eastern district of the capital," the committee's office manager, Mohammed al-Habash, told AFP.
Five other Olympic committee staffers were also set free in eastern Baghdad and left blindfolded but otherwise unharmed, Iraq's Sport Journalist Union said.
Among those still held are the Olympic Committee's chairman, Ahmed al-Hejea, its secretary-general, Amr Abdel Jabbar, the head of the Iraqi tae kwon do federation, Jamal Abdel Karim, and the head of water sports, Saeb al-Hakim.
Two guards were killed and four wounded in the raid on Saturday.
Elsewhere, a British soldier was killed and another wounded during an operation to seize a suspected "terrorist" in Basra early on Sunday.
A spokesman for the British military, Major Charlie Burbridge, said two British soldiers were wounded when they came under small arms fire. They were taken to hospital where one later died.
He said two people had been arrested during the raid, which involved a "force of significant size", but he declined to say whether the main suspect, a man "involved in terrorism activities", had been detained.
A second British military spokesman, Captain Tane Dunlop, said the operation in northern Basra had begun late on Saturday and continued into Sunday morning.