The two men, whose identities have been suppressed, now face sentences that include hefty fines and years in jail.
They were charged in early October after the 47,230-tonne Liberian-flagged Rena struck a reef about 20 km (12 miles) off Tauranga, New Zealand's biggest export port.
The Rena's captain pleaded guilty to operating a vessel in a dangerous manner, releasing toxic substances, and attempting to pervert the course of justice by altering the ship's documents, Maritime New Zealand said in a statement.
The navigation officer had denied one of the lesser charges but pleaded guilty to the rest and will face trial in May.
The men have been remanded on bail and will be sentenced on May 25. They face up to seven years in jail on the most serious charges.
The rear section of the 236-metre (775-foot) ship has fallen off the reef and is all but submerged but the bow section is still aground and wedged upright.
Salvage teams continue to remove containers off the ship and collect debris off beaches and the sea floor.
The ship spewed around 300 tonnes of thick, toxic fuel oil into the sea when it hit the reef, killing thousands of sea birds and fouling beaches up to 100 km (60 miles) from the reef.
However, salvors pumped off around 1,000 tonnes of the fuel oil and recovered nearly half of the ship's 1,300 containers.
The vessel is owned by Daina Shipping, a unit of Greece's Costamare Inc., and was under charter to Mediterranean Shipping. (Reuters)
