Maritime New Zealand announced both officers pleaded guilty to all but one of the charges. The second officer, whose name was withheld, pleaded innocent to a charge relating to the "discharge of harmful substances from ships or offshore installations."
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 the remaining containers off the vessel.
The ship spilled around 2,000 barrels of oil into the sea when it hit the reef. MNZ, the agency responding to the disaster, had removed most of the oil from the Rena by December.
The most serious charge, attempting to obstruct justice by altering ship's documents before the grounding, carries a maximum penalty of seven years in prison. The Rena's master faces four of those charges while the second officer faces three.
Both men face sentencing May 25.