Aisling Brady McCarthy spent more than two years in jail, after being accused of killing a baby she was in the care of.
Ms Brady McCarthy, originally from Lavey in Co Cavan, was charged with the murder of one-year-old Rehma Sabir at her home in Cambridge, Massachusetts, in 2013.
Rehma Sabir was pronounced brain-dead two days later.
An autopsy ruled that her death was caused by blunt force injuries to the head and the manner of death was homicide.
"Very few can fully understand the sorrow and pain that they are enduring," said a statement released on behalf of the bay's parents - British entrepreneur Sameer Sabir, and his wife Nada Siddiqui.
Leading experts in the US were called on in the trial to give evidence, with one saying that one-year-old Rehma Sabir died from abusive head injuries that could have occurred only on the day that she was admitted to hospital.
"I believe she was shaken and slammed," Dr Alice Newton told Judge Maureen Hogan. "It is my opinion that Rehma was subjected to violent force, violent shaking and blunt-force trauma such would be viewed by a spectator to be completely unreasonable handling of an infant," she said.
"After sustaining such a severe brain injury there is not an interval or period where children can look normal and then get very sick."
Ms Brady had been working illegally in the US - but she maintained her innocence throughout the murder case.
Ms Brady McCarthy's legal team had robustly challenged the charges.
And more recent medical examinations contradicted the original evidence.
The court heard that the baby had fractured vertebrae that had occurred in the weeks before her death, when she was not in the care of the Irish woman.
In an unusual move, the medial examiners reviewed investigations into the cause of death.
Last week they ordered the cause of death be changed. After an extensive review, the medical examiner said that it can "no longer rule the manner of death as homicide".