Elliot Foote, his partner Steph Weisse, and their friends Jordan Short and Will Teagle, spent 36 hours floating at sea on surfboards off the coast of Indonesia's Aceh province before they were found by rescue crews on Tuesday.
Jill Weisse described the nail-biting moment she learned her daughter was safe.
"I heard Wayne just scream upstairs and I just thought, 'Oh my god someone's rung to tell us bad news' ... And then I heard him laughing and then I heard him saying 'Hey Steph.' It was just the most unbelievable feeling," Mrs Weisse told Nine's Today show on Wednesday.
"I just was overcome with emotion to hear her voice."
After a nervous wait, footage emerged from the groups' rescue boat, showing grins from ear to ear.
"We're alive," Steph Weisse said.
Peter Foote said he received a message from his son Elliot simply reading: "Hi dad, I'm alive."
The relieved father says he just wants the group to enjoy their holiday and finish the rest of the trip.
"If the surf is great and the weather has come good and they are having a great time with their best mates, there is no point in him coming home," he told reporters.
"They are there for another eight days. Hopefully, they will feed them up and he will be back out there enjoying it. He has a great story to tell."
The rescue came after 30-year-old Elliot Foote broke away from the group in search of help, battling pouring rain, a strong current and hallucinations.
In footage shot shortly after his rescue, he described seeing his girlfriend and mates standing on a little island nearby.
"I was thinking 'oh there are my mates' ... they're waving and saying 'goodo'," Mr Foote said.
"I'm paddling to that island and I'm not making any ground.
"I'm like 'What the hell'."
The search continues for the final missing Indonesian crew member after two of the three were confirmed to have been found.
The captain of the boat, Yunardi Ardi, told the ABC his boat capsized after being hit by big waves from the back and side.
"The foreigners started paddling, we the Indonesians stayed floating, my missing friend looked weak as he was carried by a wave to the east towards Singkil," Mr Ardi said.
Prime Minister Anthony Albanese said he had contacted Indonesian President Joko Widodo to express thanks for the search and rescue efforts.
Foreign Affairs Minister Penny Wong said Australia's thoughts were with the family of the missing crew member.
The group of Australians had been in the Banyak Islands off Sumatra to celebrate Mr Foote's 30th birthday.
When tossed into the ocean, the quartet were crossing from Nias to Pinang Island, an island surf retreat.
Another boat, with eight of Mr Foote's mates, sought shelter at a small island midway before reaching Pinang and raising the alarm.
Despite the two-day ordeal, the surfers' trip will go on.
AAP with The Project.
