The four Kiwis rescued from a remote Pacific island after their yacht ran aground on a reef are safely aboard a Fiji Navy patrol boat headed for Suva.

"Thank you Fiji for your help", Maritime New Zealand said in its tweet, advising the four men were bound for the Fijian capital.

The Navy's patrol boat reached the men just after 10am, according to Maritime New Zealand.

At midday yesterday, an Air Force Orion spotted the yacht, named Jungle, beached on the reef at Tuvana-I-Ra atoll, about 425km southeast of Suva.

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The men made it to shore, where three people live, and were safe and well.

Rescue Coordination Centre spokesman Keith Allen said the crew did the right thing by taking their handheld radio with them, which meant they could communicate directly with the Orion.

The yacht is owned by Peter McLean who was on board with his son, along with Havana Coffee Works founder Geoff Marsland.

Fairfax reported the fourth crew member was co-owner of Wellington's Fidel's Cafe, Roger Young.

The 20m-long boat left Picton a week ago, heading for Tonga.

They decided to go to Fiji because of an equipment failure, then activated a distress beacon at 4am on Friday, after going aground on the reef.

The Jungle was badly damaged. A Maritime New Zealand spokesperson said it was likely it would be left on the reef to broken down by the sea.