DNA tests have proved the seven-year-old girl taken from a Roma family in Tallaght on Monday is their daughter.
The parents arrived back home with their daughter at 9:45.
The little girl was rushed into the house with a blanket over her head.
Her father spoke briefly to the media with one of his daughters translating.
She said:"I will translate for my father.
"We don't want it to happen to any family. That's all he wants to say.
"He is very happy."
Asked what the first thing the little girl said when she saw her parents, her older sister replied: "she said she was very happy. She was crying."
The family’s solicitor Waheed Mudah earlier said his clients are “absolutely delighted that their daughter is coming home.
“Her removal has been a cause of huge upset to her parents, her brothers and sisters, and the young girl herself.
“They now intend to concentrate on looking after their family and in particular trying to reassure their daughter that she will be left in their care.
“All that being said however, our clients also wish to say that they do not believe that what has happened to their family over the last few days should ever have happened.
“They do not accept that this was any proper or sufficient basis to take their daughter away from them, thereby causing her and them the upset which has been caused.”
He added that they are “very conscious of the fact that this case has been linked with events in other countries which have nothing to do with them, and that there has been a vast amount of publicity about their situation.
“They are also conscious of the fact that it is going to be difficult to try to return to normal life.
“They believe that there are very serious questions arising about the procedures used in this case but are going to wait for things to settle and then consider their position, and that of their daughter in light of recent events, and will be taking legal advice in respect of this.
“Finally our clients would like those who hear this statement, and particularly those who are parents themselves, to consider how they would feel if one of their children was taken away in similar circumstances for similar reasons.
“They hope that no other family has to go through the experience that they have just suffered.”
A 21-year-old sister of the child, who can not be identified for legal reasons, said she didn't want any family to suffer a similar ordeal.
"Everyone was very sad," she said. The sister said she hoped no other family would have to go through a similar ordeal.
"The most important thing now is that my sister is coming back," she said. The sister said she supported calls by human rights campaigners for an independent investigation into the cases.
She added that neighbours, family and friends were very supportive to them during the last number of days.
"We are very happy," she said. "We will have a big party. We will have music, dancing, everything."
She said she hoped no other family would have to go through the same experience.
Asked if she supported Pavee Point’s call for an independent investigation into the incident, she said “yes of course”.
Minister for Justice Alan Shatter has asked the Garda Commissioner Martin Callinan for a report into how two children were taken from their biological
An Garda Síochána released a statement this evening which read: "Protecting vulnerable children is of paramount importance to An Garda Síochána and we continue to work in partnership with the HSE and other agencies to ensure children’s safety.
"An Garda Síochána has a published and comprehensive policy which remains under constant review into the investigation of sexual crime, crimes against children and child welfare, which provides for an effective and coherent approach to the investigation of this sensitive and challenging area.
"An Garda Siochana want to assure the community that we take extremely serious all reports received from members of the public concerning child welfare issues.
"In all cases immediate steps are taken to protect the welfare of the child in accordance with relevant statutory provisions and obligations."
The girl was dramatically removed from a Roma family's home in Tallaght, Dublin, on Monday after a tip-off to gardai that she did not look like the rest of the family.
The child, who spent two nights in the care of the HSE, has now been reunited with her family.
Tests conducted this afternoon confirmed that she is the biological daughter of the Roma couple with whom she had been living.
The Roma family, who said that she was born in the Coombe Hospital in Dublin in April 2006, have now been vindicated.
The Roma couple gave their consent to DNA tests being carried out last night.
They were taken to a garda station where they gave samples through mouth swabs.
The girl was also tested in the presence of HSE officials.
The results were sent immediately to the forensic laboratory at garda headquarters before the results revealed that the girl was related to the Roma family today.
The girl was taken from the house in Tallaght, in south Dublin, on Monday afternoon and placed in the care of the HSE.
The girl's sister said she belonged in the Tallaght house and had been living with them since the day she was born in 2006.
She said the girl attended a local school and had been watching TV on Monday afternoon when around a dozen garda officers and HSE officials arrived.
"Everybody was shocked, even all the children in the house," said a brother-in-law of the young girl.
"She didn't want to go with them. She was asking us, 'Why? Why they take me?"
Gardai visited the house after they received a claim from a TV3 journalist - via the public - that the seven-year-old girl was not the householders' daughter.
The journalist was given the information about the girl, who is blonde and has blue eyes, on Facebook.
During a two-hour visit to the house, officers interviewed the two adults about the girl and sought proof that she was their daughter.
They had concerns about the child's identity, and as a result of the interview and their attempts to check out the information given by the adults, they decided after two hours to use emergency powers contained in section 12 of the Child Care Act to take the girl from the family and hand her into the care of the HSE overnight.
The family produced a passport for the girl, but the photo used was of a small child and could not be immediately matched with the girl.
Gardai were also told by the family, who have other children, that the girl was born at the Coombe Hospital in 2006, but preliminary checks could not confirm that.
However, an independent examination by the Irish Independent of the Coombe records yesterday showed that the woman had given birth to a daughter on the day she mentioned in 2006.
At the time of the birth, the parents of the infant did not live in Tallaght, but had another address in Dublin. They have been residing in Tallaght for several years.
The child's first name on the birth record differed from the name used by the girl, but it was accepted that this was not unusual.
Gardai said last night that plans to carry out a more detailed interview with the Roma couple were being put on hold, pending the DNA results.
The garda investigation was launched after another Roma couple, accused of abducting 'Maria', a four-year girl with blond hair and blue eyes, told a Greek court that the child's biological mother had given her to them as a baby because she could not look after her.
DNA tests showed that 'Maria' was not born to the couple, who were arrested after police raided a Roma camp in search of drugs and weapons and found the girl.
Earlier a two-year-old boy was removed from his family home in the midlands town of Athlone overnight but was returned to his parents following inquiries by gardai.
A human rights group has called for an independent inquiry amid claims the two Roma children were "abducted" from their families by authorities.
Pavee Point fears there is hysteria after the case of a blonde-haired, blue-eyed girl named Maria was found with a Roma family in Greece and accused gardai and health chiefs of racial profiling.