As the world was ushering in 2014, the men were swapping the austere, remote military facility in southeastern Cuba for a refugee camp in their new homeland.
"They are already in Slovakia. They will now stay at a camp for migrants, learn Slovak and get ready for a new life," interior ministry spokesman Ivan Netik told AFP.
Yusef Abbas, 38, Saidullah Khalik, 36, and Hajiakbar Abdul Ghuper, 39, were the last of a group of 22 ethnic Chinese Muslims captured in a mountain camp in Afghanistan in 2001.
"The inmates we received were never suspected, let alone convicted of crimes," Netik said, adding the authorities were looking for jobs for them.
The releases, part of stepped up efforts by the administration of US President Barack Obama to fulfill a long-held pledge to close the jail, were announced earlier Tuesday by the Pentagon.