"She sounded tired, a little bit small in her voice, but she was able to make jokes and she was looking forward to getting some sleep," her mother, Marianne Sunderland, told reporters outside the family home in Thousand Oaks, California.
The 16-year-old had to abandon her sailboat, Wild Eyes, when a French fishing vessel rescued her more than 2,000 miles (3,200 kilometers) from the western Australia coast, two days after she lost communication with her family and sent out distress signals. She will spend more than a week traveling to Reunion Island, a French territory east of Madagascar.
"Crazy is the word that really describes everything that has happened best," Abby Sunderland wrote Saturday morning in a blog post from "a great big fishing boat headed I am not exactly sure where."
"The long and the short of it is, well, one long wave, and one short mast," she wrote.
Sunderland had been stranded in heavy seas since Thursday, when she set off a distress signal after the mast collapsed. Laurence Sunderland said the family was not going to elaborate on the problems that led to the emergency, and Abby Sunderland didn't provide details in her blog post.
The Australian Maritime Safety Authority said the French ship Ile De La Reunion brought Sunderland on board from her stricken craft Saturday afternoon at the site (about 2:45 a.m. PDT, 0945 GMT).
French authorities called it a "delicate operation," and said at one point the fishing boat's captain fell into the ocean and had to be rescued. Laurence Sunderland said the crew used its dinghy in the transfer.
Australian authorities were broadcasting a message to boats crossing through the area warning them that Sunderland's sailboat is still adrift.
Sunderland will leave the French fishing boat in about two days to board a maritime patrol boat that will take her to Reunion Island, according to a statement from the office of the French Indian Ocean island's top official. The transfer will take place off the Kerguelen Islands, with the exact timing depending on weather and ocean conditions.
Authorities said Sunderland likely would not arrive in Reunion for at least a week.
Despite a lag in getting to see her, Laurence Sunderland said the family is "just ecstatic that she is alive and well and survived the ordeal."
Sunderland set out from Los Angeles County's Marina del Rey on Jan. 23, trying to become the youngest person to circumnavigate the globe solo and nonstop.
Soon after starting her trip, Sunderland ran into equipment problems and had to stop for repairs. She gave up the goal of setting the record in April, but continued, hoping to complete the journey.
Zac Sunderland, her brother, held the record for a little more than a month last year until Briton Mike Perham completed his own journey. The record changed hands again last month, when 16-year-old Australian Jessica Watson completed her own around-the-world voyage.
Outside the family home early Saturday, eight pink balloons were tethered to the white picket fence in front of the single-story house and beneath them was placed a large, hand-painted sign that read: "Thank God Abby's alive."
She had been keeping in contact with her parents through satellite communications and had made several broken calls to them, reporting her yacht was being tossed by 30-foot (9-meter) waves -- as tall as a 3-story building. An hour after her last call ended Thursday, her emergency beacons began signaling.
Rescuers in a chartered jet flew from Perth on Australia's west coast and spotted Sunderland's boat on Thursday. She was able to radio to the plane to say she was in good health and had plenty of food supplies.
Her parents have come under criticism from some observers for allowing the high-risk adventure.
Veteran sailors questioned the wisdom of sending a teenager off alone in a small boat, knowing it would be tossed about for 30 or more hours at a time by the giant waves that rake the Southern Hemisphere's oceans this time of year.
Her father defended the voyage, and Abby Sunderland said it seemed everybody was "eager to pounce on my story now that something bad has happened."
"As for age, since when does age create gigantic waves and storms?" she wrote Saturday.
The Australian maritime authority did not say how much the rescue mission would cost but said it would not be seeking compensation for the search, which initially fell just outside of Australia's search and rescue region. It was not immediately clear if the French vessel would seek compensation.
Family spokesman Jeff Casher said Sunderland's vessel was so badly damaged, her attempt to circle the globe was over.
"This is the end of the dream. There's no boat to sail," he said.
For Sunderland, that reality was still sinking in.
"I keep hitting the wrong keys and am still trying to get over the fact that I will never see my Wild Eyes again," she wrote on the Saturday morning blog posting. "So I'll write more later."
Her father said he had no doubt she'll be back on the water soon.
"Abby has been raised on the ocean," Laurence Sunderland said. "This was like second nature. She'll be back."