A post on the family's Facebook page says Binh Wagner received her "gift" from an anonymous donor, though the timing of the surgery is being kept secret to protect the donor's privacy.
The girls suffer from Alagille syndrome, a genetic disorder that affects vital organs. Without a liver transplant, the girls would die.
Binh's twin sister Phuoc returned home from hospital last month after receiving part of her father Michael Wagner's liver.
Their story made headlines around the world when the family said it couldn't possibly decide which daughter would get the transplant, so they left it to doctors to pick the best candidate based on medical reasons.
The family went public with a plea to find a second donor for Binh. The response was overwhelming, with nearly 500 people contacting Toronto General Hospital to offer parts of their liver to the little girl.
Dr. Gary Levy, who runs the liver-donor program at the hospital, said shortly after the appeal that they had identified a handful of candidates for Binh.
Phuoc, who received the new liver in mid-February, remained in hospital for about a month as she recovered and fought off a few illnesses.
The changes in Phuoc were startling, Wagner told The Canadian Press last month. Her complexion was no longer a yellow hue.
"You can see the white of her eyes — we've never seen them,'' Wagner said. The constant scratching has stopped and she was finally sleeping through the night.
The family wrote on Facebook Monday that Phuoc has recently managed to sleep without her feeding pump.
The family also said on Facebook that Binh is "recovering well, at her own pace," despite experiencing "very different medical issues" from her sister.
"We are looking forward to all being reunited and leading a healthier life now, with both transplants finally behind us," the post reads.
The family could not immediately be reached for comment, but is planning a news conference Tuesday morning with doctors from Sick Kids and Toronto General hospitals.Suggest a correction