The ransom delivered on Sunday is believed to be between $5.5m and $7m, according to unnamed sources interviewed by the Reuters news agency.
With 28 crew members on board, the Maran Centaurus oil tanker was captured in November as it was crossing the Indian Ocean, northeast of the Seychelles islands.
The tanker was sailing from Kuwait to the United States.
The European Union's anti-piracy force says the crew includes one Romanian, two Ukrainians, nine Greeks and 16 Filipinos.
Andrew Mwangura of the Kenya-based East African Seafarers' Assistance Program told journalists in December that the hijacking was a "jackpot to the pirates" because a tanker full of oil is worth millions of dollars.
The Greek ship was the second largest oil tanker seized by Somali pirates.
In 2008, pirates hijacked the Saudi-owned Sirius Star. They eventually released the ship for a reported $3m ransom.
World powers, including the European Union, Nato and the United States are running naval patrols off the Somali coast in an effort to protect commercial shipping.
In response, the pirates have extended their reach, attacking ships up to 1,800km from Somalia, deep in the Indian Ocean.