The men, who arrived in Uruguay early Sunday in a deal aimed at helping the United States close the military prison, underwent medical exams at a military hospital on arrival.
"That's the only reason they're not walking around the streets of Montevideo today like any neighbor's son," Defense Minister Fernandez Huidobro told local radio station Carve.
The six former inmates- four Syrians, a Palestinian and a Tunisian- spent more than a decade at the detention center set up in the wake of the 9/11 attacks. They had been cleared for release but the US ruled they could not be sent to their home countries for security reasons.
One of the men described his experience in a letter published in a Uruguayan newspaper today.
"My name is Abdelhadi Omar Faraj. For the past 12 years I've also been known as prisoner number 329 at Guantanamo. And I am one of the men who recently arrived as refugees in Uruguay from that horrible prison," the Syrian man wrote in a letter sent to the Spanish newspaper El Pais by his lawyer in New York.
Faraj described leaving home at 19 years old to seek work in Iran and avoid mandatory military service in Syria, eventually moving on to Afghanistan.
"When the war in Afghanistan broke out in 2001, I feared that one of the warring parties, the Northern Alliance, would kill me for being an Arab. I fled overland to Pakistan," he said.
He said he was arrested at the border by Pakistani soldiers, handed over to the US army and detained in "sub-human conditions" in Kandahar.
In June 2002, he was flown to Guantanamo.
In 2009, a military, FBI and CIA team cleared him for release, he said. But he was unable to be sent to Syria, by then in the grips of civil war.
"If it hadn't been for Uruguay, I would still be in that black hole in Cuba," he said, thanking the country and President Jose Mujica for accepting him as a refugee.
"I want to assure you and all Uruguayans, including the Uruguayan government, that we bear only good will and positive contributions for Uruguay while we learn Spanish and remake our lives here," he said.