At the time when they captured the Ukrainian vessel, pirates had demanded $20 million in ransom. However, reports remain unclear as to how much Ukrainian officials will pay for its release.
Sugule Ali, a spokesman for the pirates who captured the ship, said: "I can't tell you what the ransom is, but what I can say is that an agreement has finally been reached.
"We have no doubt this problem will be resolved and I hope the owners will honour the last remaining points."
Ali said said on Tuesday they had lowered their ransom demand to $3 million.
In another high-profile hijacking, pirates forcibly boarded the Sirius Star on November 15.
The Saudi supertanker was loaded with oil worth $100 million and its capture is the biggest in the history of maritime hijacking.
Pirates holding the Sirius Star said on Saturday they were hoping for a "favourable" response to their $25 million ransom demand, ahead of a deadline which expires on Sunday.
Mohammed Said, the leader of the group that seized the ship, said negotiations to free the vessel were ongoing, but he did not know when they would conclude.
Shipping firms have opted to re-route to the Cape of Good Hope because of the seizure of several ships across the Gulf of Aden, causing delays and increasing costs.
Ethiopia had called for stronger international action against piracy off the coast of Somalia.
Despite the presence of foreign navies in the Gulf of Aden and the Indian Ocean, hijackers have defied them and seized ships, the latest being the Biscaglia, a Liberia-flagged oil and chemical tanker which had been captured on Friday.