The announcement, carried by Syria's official news agency SANA, said the guards were handed over to the Syrian side on the Syrian-Iraqi border and taken to hospital for further treatment.
The spokesman, whose identity was not provided, did not specify in the statement when the hand over occurred or where it took place. No other details were immediately available.
Syrian Foreign Minister Farouk al-Sharaa had said Sunday that Syria wanted to avoid escalating tensions with the United States and was instead engaged in quiet diplomacy over the return of the border guards.
The June 18 border clash, during which U.S. forces attacked what they suspected were fleeing officials of Saddam Hussein's deposed regime near the desert border post of Abu Kamal, threatened to stoke already strained relations between Washington and Damascus.
Syria was a loud opponent of the U.S.-led invasion of Iraq, while U.S. officials at one stage accused Damascus of harboring fleeing former Iraqi officials and sending weapons to Saddam's forces — claims Syria rejected.
"This subject has had media attention more than it deserved," al-Sharaa said at a press conference Sunday.
He said Syrian and U.S. officials had been discussing the fate of the five soldiers, three of whom were seriously injured and taken to a military hospital in Baghdad. The other two were treated in western Iraq. One Iraqi was also killed in the attack, U.S. officials have said.
On Saturday, the U.S. Embassy in Damascus said the State Department was working with the Pentagon regarding the "timing and particulars of the repatriation of the five Syrian border guards."
U.S. officials have been unable to explain the full circumstances of the attack, including why houses in a nearby village and the vehicles were struck and who was being targeted.
By Zeina Karam