The Panamanian-registered Probo Koala was impounded on September 27 in the Estonian port of Paldiski, following a request by Ivory Coast.
Thousands of people in Ivory Coast suffered vomiting, stomach pains and other symptoms caused by toxic fumes from waste from the ship in late August, according to the government.
A spokeswoman for the prosecutor's office said: "The environment inspectorate said that the ship has been correctly unloaded and we gave permission for the ship to leave."
Estonia has mounted a criminal investigation, suspecting that the tanker had failed to declare the actual content of the slops it had sought to unload at the Estonian port.
Although the investigation is continuing, the state prosecutor's office said it was no longer necessary to hold the vessel in Estonia.
The Probo Koala, chartered by the Netherlands-based shipping company, Trafigura Beheer, last month offloaded more than 500 tonnes of waste - reportedly a mixture of oil residue and caustic soda used to rinse out the ship's tanks - in Abidjan in Ivory Coast.
An Ivorian company which was supposed to properly dispose of the waste dumped it on several refuse sites in the city of four million people, sparking a health crisis which has seen a steadily climbing casualty toll.
Officials in Ivory Coast said on Friday that another two people had died as a result of the toxic sludge scandal, taking the number of fatalities to 10, while 69 were still in hospital and more than 102,000 have sought medical help.
Trafigura, said it was carrying routine petroleum "slops" from the inside of oil tanks and had not breached proper procedure in Africa.
The company said in a statement: "The Probo Koala followed all correct procedures when it offloaded slops at Abidjan."
The incident stretched the country's health services and led to the resignation of the cabinet, although most were later reinstated.