The US ambassador to Hungary said Boban Milen Kovic and Sesko Tairovic had been well treated, and Red Cross officials said the soldiers had assured them they did want to go home - although there is no guarantee they won't be put back on the front line.
None of the dozens of reporters gathered at the border post for the handover saw the two men, who crossed into Yugoslavia from the Hungarian point of Roeszke to Horgos on the other side.
Red Cross officials said the two were kept away from reporters under rules which forbid putting "pressure" on captives. They also refused to say if the two men had been in contact with their families.
"They looked in good health," an ICRC spokeswoman Nadya Kebir said.
She said that under the Geneva Convention covering treatment of prisoners of war, released soldiers are not supposed to be returned to combat. "But we can't control that."
The soldiers were captured separately last month by the rebel Kosovo Liberation Army in Kosovo and handed over to Nato. The men were held at Mannheim, a US base in Germany, and allowed regular visits from the Red Cross, US ambassador Peter Tufo said.
"The Serbs PoWs were well cared for, were provided with medical care, had the opportunity to send and receive mail and had their habits, customs and religious practices respected," he added.
Although US officials have said there is no link between freeing the two Serbs and the release by Yugoslavia this month of three US army soldiers captured on 31 March along the Kosovo-Macedonia border, Mr Tufo contrasted the treatment of the two sets of prisoners. "The American PoWs were physically mistreated at the time of their capture and during interrogation," he said.Reuse content