Last month, lawmakers in the island republic voted against granting Fischer citizenship, instead offering him a special foreigners' passport and rights of residency That move, however, was not enough to convince Japanese authorities to release Fischer from detention.
He is being held in Japan on alleged passport violations.
Bjarni Benediktsson, a member of a parliamentary board reviewing Fischer's request, said Friday citizenship will be granted next week.
U.S. prosecutors have been seeking access to Fischer for allegedly violating economic sanctions against Yugoslavia by playing Russian chess master Boris Spassky in 1992.
Beautician charged with giving client fatal silicone butt injection
Attkisson leaves CBS News, reportedly over network's 'liberal bias'