Abdel Rahman, who led the militant Al-Gamaa al-Islamiya group in Egypt before immigrating to the United States, had been sentenced in 1996 for conspiring to bomb civilian targets in the country.
Seen as a jihadist spiritual leader, he had also been seen as inspiring the 1993 bombing of the World Trade Centre that killed six people.
"We have contacted the American and Egyptian authorities to repatriate" his body, his son Mohamed Omar told AFP.
Following his election victory in 2012, Egypt's Islamist president Mohamed Morsi demanded at a rally the cleric's release.
Morsi was toppled by the military a year later.