Rena struck a reef off the coast of New Zealand in October. It broke apart earlier this year and salvage teams are working to get remaining shipping containers off the vessel.
The ship spilled about 2,000 barrels of oil into the Bay of Plenty when it hit the reef. Maritime New Zealand, the agency responding to the disaster, had removed most of the oil from the ship by December.
MNZ announced Master Mauro Balomaga and Second Officer Leonil Relon pleaded guilty to a total of 11 charges stemming from the grounding.
"This grounding has had significant consequences for the Bay of Plenty community and the country as a whole," MNZ Director Keith Manch said in a statement. "Today marks a milestone in the response, which is still under way."
MNZ said assessments of the wreck confirmed the threat of an additional oil spill from Rena was minimal and the threat to the environment was low.
The owner of the vessel, Daina Shipping Co., which has headquarters in Greece, faces an $8,100 fine for every day harmful substances were discharged.