"Once the Polish speaker - who was known to the man - made radio contact with him, he was able to convince him of the gravity of the situation and he agreed to leave his boat."
The crew of the Key Opus dropped a net down the ship's side to allow the man to climb up, while the Orion continued to circle overhead.
NZDF said the 10.6m yacht was on a solo round-the-world voyage, and had left Auckland on March 18. It was headed towards Cape Horn when it encountered major problems.
Weather conditions in the area have been rough throughout the operation, with 25 knot winds and a three-metre swell.
The RCC is broadcasting a warning for other vessels that the man's yacht is drifting in the area.
The alarm was activated 2660km east of Christchurch on Thursday, and the RCC has been managing the search since then.
"The fact it took two full days of sailing for the Key Opus to reach the man's position underscores the remoteness of this rescue," Wilson said.
"The man was in good spirits and understandably very happy to be rescued."
The man is now being taken to Chile, where he is expected to arrive on May 4.