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The chances of another successful refloat were unlikely, said the statement.
The whales, the last of a pod of up to 99, had been ashore for five high tides and had twice been refloated with the assistance of DOC staff and volunteers.
"The whales are now in noticeably poor condition and there is a gale warning in force for this afternoon, meaning that an assisted refloat would not be possible. A decision has therefore been made to euthanize the surviving whales," it said.
Kimberley Muncaster, chief executive of the Project Jonah whale rescue group, described the regrounding as "tragic."
The euthanizing of the whales brought the total death toll from the stranding to 82, she said in a statement.
"We must now focus our efforts on the 17 whales that refloated themselves on Monday night, and make sure they remain safe," she said.