"Our crew established communications with the skipper. He reported a problem with the vessel's helm and appeared to be in good spirits," Webb said.
"It's always great to successfully conclude a search, especially so far from home and over the Easter break, which is a time for family and friends."
The yacht's helm had broken in high seas, crippling the vessel which could no longer be steered.
A cargo ship, MV Key Opus, has now been diverted to rescue the sailor. It was expected to arrive at the mid-ocean rendezvous early Saturday.
The New Zealand Defence Force said the 10.6m yacht was on a solo round-the-world voyage.
The Rescue Co-ordination Centre said the vessel had left Auckland on March 18 and was headed towards Cape Horn when it encountered major problems.
Earlier Webb said an Orion from Whenuapai was expected to arrive at the yacht about mid-morning.
"Our priority is to locate the yacht, establish communications with the skipper and provide assistance if required," Webb said.
Once the Orion found the yacht, relayed its position to a commercial vessel in the area that the Rescue Co-ordination Centre had already asked to come to its aid.
Webb said the commercial vessel was expected to reach the yacht tonight.
The stricken yacht has a VHF radio and a life raft. The Air Force said it activated its distress beacon about 3pm on Thursday.