The high-risk mission to recover the bodies left behind after Monday's deadly eruption started at 8am.
Police national operation commander Deputy Commissioner John Tims said the process to transport them to the navy ship by helicopter had begun.
He said one body had been successfully recovered and is now on board HMNZS Wellington.
The operation to recover the remaining bodies continues.
Earlier police said they expected the recovery operation to continue for another couple of hours.
Conditions for the operation were good in regard to the weather, sea state and the environment on the island.
Police Deputy Commissioner Mike Clement said the volcano is quiet, which is the critical thing, and there is just a light wind.
A team of eight Defence Force personnel have been involved in the recovery mission.