"They've received an answer from the Swedish embassy that the DNA test proved they are Haddile's parents," the couple's lawyer, Fatima Benbraham, told the Aftonbladet newspaper.
She expects the couple to come to Sweden on December 7th.
Carl-Olof Lindberg, who represents Haddile, told TT he has warned the social services administration in Lund to be ready for every possible scenario when the toddler's birth parents arrive.
"The Algerian couple might just come here to simply pick up the girl and say thanks a lot for your time. It's going to be terribly traumatic for her because she doesn't have any memory of her parents, has never been to their home homeland, and doesn't speak their language."
The social services office's investigation will ultimately determine if Haddile should continue to be cared for by the foster parents with whom she has lived for nearly her entire life.
The case of 2-year-old Haddile, who was abandoned by her mother shortly after her birth and then allegedly abused by her stepfather before being taken in by foster parents, has outraged and captivated Swedes.
The girl's mother, who is Algerian but has French citizenship, disappeared 20 days after giving birth at a hospital in Lund in the south of Sweden.
Haddile's step-father took care of her when the mother disappeared but he was accused of abuse after the baby girl was admitted to hospital with serious brain damage at the age of four months.
The child then ended up in foster care and her foster parents have said they are willing to adopt her.
A move by the Migration Board (Migrationsverket) to deport the child to France in an effort to reunite her with her mother resulted in a petition signed by tens of thousands of Swedes, prompting the agency to put a temporary delay on their deportation decision as the search for her parents continued.
If social services decide that the girl should be reunited with her birth parents, Haddile's case would no longer be a matter for migration authorities.
Citing a report from the Swedish Foreign Ministry, Lindberg fears that, since Haddile was born out of wedlock, she will be traumatized and suffer for the rest of her life in Algeria.