The Maritime Union of New Zealand says it has cleared the TPC Wellington to leave Marsden Point after working with crew members to arrange their repatriation.
Two crew members died on the log ship on Monday from what is thought to be asphyxiation, but investigations into the accident are ongoing.
Maritime Union General Secretary Joe Fleetwood says the priority has been to ensure the welfare of remaining crew members.
He says an agreement has been reached between the company and the crew with the assistance of the ITF and Maritime Union.
The Burmese crew members would return with the vessel to Korea where the company would release them from their contract.
The crew members would be paid wages owing, repatriation costs and a bonus.
Under the agreement they would be able to refuse to carry out work they felt was unsafe.
The Maritime Union is affiliated to the International Transport Workers Federation (ITF), which represents seafarers and maritime workers around the world.
ITF New Zealand Inspector Grahame McLaren arrived at the vessel on Tuesday afternoon and had been working with crew since that time.