"The five detainees that Kuwaiti authorities received today are on their way to Kuwait on a flight," the agency, KUNA, quoted the Kuwaiti ambassador to the United States as saying on Thursday.
"They're expected to be tried in a Kuwaiti court where they will receive a just sentence."
The five detainees were among a dozen Kuwaiti men initially imprisoned at the US military prison during the 2001 US-led war to oust al-Qaida and the Taliban from Afghanistan after the 11 September attacks.
One former detainee Nasser al-Mutairi was freed last January, but was later tried and acquitted of charges of undermining Kuwaiti security, weapons possession, joining al-Qaida and fighting a friendly nation, a reference to the United States.
But on Wednesday, a Kuwaiti appeals court sentenced al-Mutairi to five years in prison for "participating in hostile activities against a friendly country", "weapons and ammunitions training and possession" and "hurting Kuwait's political position".
Kuwait, a staunch US ally, is a main transit route for American forces going to Iraq.
It was a launch pad for the 2003 war on Iraq and up to 25,000 US soldiers are based there.