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.
Earlier today, Maritime New Zealand said the Fiji Navy would rescue the men at first light this morning.
The yacht is owned by Peter McLean who was on board with his son, along with Havana Coffee Works founder Geoff Marsland.
Fairfax reported that the fourth crew member was co-owner of Wellington's Fidel's Cafe, Roger Young.
Roger Foley, who knows both Marsland and McLean and has crewed on the yacht, said yesterday that he was glad to hear the men were safe.
"It's great that the crew is okay, but very sad that Jungle is damaged."
He said McLean was a "very experienced" sailor.
The 20m-long boat left Picton a week ago, heading for Tonga.
They decided to go to Fiji last night because of an equipment failure, then activated a distress beacon at 4am on Friday, after going aground on the reef.