Monsoon rains in recent weeks may have prevented the pair from dying of thirst.
The men, 22 and 24, were rescued from the Torres Strait by a helicopter Saturday and flown 57 nautical miles (66 miles; 106 kilometers) southeast to a hospital on Thursday Island off Queensland state, Maritime Safety Authority spokeswoman Tracey Jiggins said.
A photograph taken from the patrol plane shows both men standing shirtless in their pink ice box - a waist-high container barely larger than a bathtub and often used to store freshly caught fish - and waving frantically.
"These two people being spotted is miraculous in itself in the huge expanse of ocean after drifting for 25 days," Jiggins said.
Authorities have not said what the men ate or drank during their ordeal. Media reports have said they survived on fish chunks that had been stored in the cooler before the boat sank and rain water that pooled on the floor.
Greg Edwards, a Thursday Island commercial boat operator, said there had been a lot of rain in Torres Strait since Christmas, and 50-knot (58-mph; 93-kph) gusts that chopped up the seas.
"It's been pretty miserable weather," Edwards said.
The men told police they had been aboard a 30-foot (9-meter) wooden fishing boat that sank Dec. 23 with a total of 20 crew from Thailand and Myanmar, also known as Burma.
Jiggins said the men found refuge inside a large insulated box that held ice on the boat. "At the time of the sinking, the two survivors also witnessed other crew in the water with no flotation devices," she said.
One of the rescuers, pilot Terry Gadenne, told Seven Network television that each man drank about four pints of water within seconds of being hoisted aboard the helicopter.
"They were dehydrated, there's no doubt about it, and very keen to get out," Gadenne said.
The men were treated for dehydration at Thursday Island Hospital and released Tuesday.
Immigration Department spokesman Sandi Logan said the men would likely be kept under department supervision while officials determined their identities. Neither man had identity documents.
The Myanmar Embassy in Canberra said it had not contacted the men and did not intend to make a public statement about the incident.
Officials did not know why the fishing boat sank, Jiggins said, but the two men said the vessel had been taking on water for some time before it went down.
The survivors were not able to provide accurate details of where the boat sank. Australian authorities did not plan to search for other survivors.
"We've made an assessment ... that the remaining crew members would not be able to survive 25 days in the water without any form of flotation device," Jiggins said.
Graeme Reberger, director of the Australian ice box manufacturer Techni Ice, said the men appeared to have been in one of his company's 800-liter (210-gallon) models manufactured in Thailand.
"I'm just surprised that they were able to stay in it without it tipping over," Reberger told Nine Network television news.
