Raudhatul Jannah, then aged four, and her seven-year-old brother were carried away clinging to wooden planks when huge waves struck their home in Aceh province on December 26, 2004.
The children's mother, Jamaliah, and her husband survived the quake-triggered tsunami that killed tens of thousands in Aceh, on western Sumatra island, and had long ago given up hope of finding their children alive.
But in June, Jamaliah's brother spotted a girl in an Aceh village walking home from school who bore a striking resemblance to Jannah.
He made inquiries and found out that the girl had been caught up in the tsunami, and was swept from Aceh to remote islands southwest of the province. She was taken back to the mainland by a fisherman, whose elderly mother raised the youngster.
Jannah's parents, who moved to the neighbouring province of North Sumatra following the tsunami, travelled to Aceh soon afterwards to meet the girl, and firmly believe it is their missing daughter, now aged 14.
Jamaliah, who like many Indonesians goes by one name, on Thursday said it was a "miracle" her daughter had been found and described how she could not stop the "tears from flowing" during an emotional reunion.
'We felt the bond right away'
Jannah this week moved to North Sumatra to live with her birth parents, and the couple say they are now hopeful they can find their son. "We are very hopeful we can find her brother," Jannah's father, Septi Rangkuti, told reporters. "We have reported our son missing to the police so they can help us find out his whereabouts."
Rangkuti, 52, believes his son Arif Pratama Rangkuti may still be on the Banyak Islands, an archipelago some 100 kilometres (60 miles) from the Aceh coast where the children ended up after being swept away.
For around a year, they lived with fishermen and their families on the islands. A fisherman wanted to adopt both of them, but ended up taking just Jannah as he did not think his family could provide for two more children. His mother, Sarwani, was the one who mainly cared for Jannah when she was growing up.
Rangkuti admitted he did not believe his daughter could be alive when his brother-in-law first spotted Jannah. "There's no way that's my daughter, I thought, because it had already been 10 years," he said, speaking in the capital of Aceh province, Banda Aceh, where the family had travelled to meet journalists.
But he went on: "When we saw her, we knew, we felt the bond right away." He added, "If we need to do a DNA test, then we are prepared to, if people don't believe us. But we are sure she is our daughter."
Jannah, who appeared shy and overwhelmed by the media attention, told reporters: "I am very happy I can be with my mother and father again." She also said she was happy to meet her younger brother, who was born after the tsunami, for the first time.
Sarwani, who goes by one name, said Jannah's adoptive family were delighted the teenager had found her birth parents. "We are very happy they have reunited. She will always be part of our family, and actually, we now all feel like one big family," she said.
The tsunami killed more than 170,000 people in Aceh, which was the worst-hit area, and tens of thousands more in other countries around the Indian Ocean.