Fawzi al-Odah had been one of just two Kuwaitis still detained in the holding centre for US "war on terror" prisoners that President Barack Obama has long promised to shut down.
"Fawzi arrived early this morning. He is in good health," Khaled al-Odah told AFP.
Odah said his son, 37, was taken straight to a military hospital for a checkup.
After a week, he will be transferred to a government-run rehabilitation centre for an unspecified period but his close relatives will be allowed to visit him.
Fawzi, still unmarried, was greeted at the airport by his father and two brothers. At the military hospital, around 40 family members, including his mother and grandmother, were allowed to visit him.
Activists posted pictures of him embracing his mother and kissing her head. Another photograph showed him with his young niece.
His father had led a support group for the families of the Kuwaiti prisoners at Guantanamo.
He has always maintained that his son was an aid worker and never took part in any fighting in either Afghanistan or Pakistan, where he was captured in late 2001, that might warrant any allegation of being an enemy combatant.
Fawzi was seized by tribesmen in northern Pakistan, who sold him to the Pakistani army, which in turn handed him over to the United States.
Signup to our newsletter and follow us on Facebook and Twitter!
He was captured alongside compatriot Fayez al-Kandari, who is now the only Kuwaiti still held at Guantanamo.
Fawzi was the first inmate freed since late May. His release was cleared by the Periodic Review Board in July.
The same body advised against releasing Kandari, ruling that he "almost certainly retains an extremist mindset and had close ties with high-level Al-Qaeda leaders in the past."
The Obama administration said on Wednesday that it plans to speed up releases from Guantanamo.
"The Department of Defence hopes to transfer more than a dozen detainees to countries in South America and Europe, in the next two months, through the winter," a Pentagon official told AFP.
The official, who asked not to be named, said countries have agreed to take around 20 Guantanamo inmates, although the deals are not yet finalised.
Another US defence official said the administration was "working diligently to transfer the remaining detainees from Guantanamo."
"Closing Guantanamo is a priority for the defence department," Lieutenant Colonel Myles Caggins told AFP.