An official statement said that the decision was made by the US government after talks between Sheikh Sabah al-Ahmad al-Sabah, the amir of Kuwait, and George Bush, the US president.
The men were identified as Omar Rajab Amin and Abdullah Kamel al-Kundari by Khaled al-Oudah, a spokesman for a group representing the detainees’ families in Kuwait.
Al-Oudah said the US and Kuwait were currently still in negotations over the remaining four Kuwaiti inmates, one of whom is his son, Fawzi.
A total of 12 Kuwaiti men have been held in Guantanamo Bay since the detention centre was created after the US-led invasion of Afghanistan in late 2001.
In May this year, a Kuwait court cleared five Kuwaitis formerly held in Guantanamo Bay of charges of belonging to al-Qaeda and ordered the men freed, although the prosecution has said it will appeal.
Kuwait, a US ally, is the main transit route for US forces going to Iraq and the launch pad for the 2003 US invasion of the country. Up to 25,000 US troops are based in the country.
About 450 detainees are still being held at Guantanamo Bay, which has been heavily criticised by human rights groups after the US government ruled the inmates to be “unlawful combatants”, which meant that their human rights were not protected under the Geneva Convention.
However, last week the US Pentagon reversed this policy.