Mohamed Said, who said he was one of the pirates, told The Times of London by telephone that everyone on board the Sirius Star had been freed unharmed.
The tanker was captured in the Indian Ocean 420 miles off the coast in November. The pirates sought $25 million for its release but later cut their ransom demand to $3.5 million.
The ship was owned by Vela International Marine, a subsidiary of Saudi Aramco. Vela refused to comment on any payments, but pirates said that their demands had been met.
Andrew Mwangura, head of the Seafarers' Assistance Program in the port of Mombasa, Kenya, said that the Sirius Star, more than 1,000 feet in length, is too big to dock in Mombasa. He said that the vessel might simply continue on its voyage, rounding the Cape of Good Hope.