The child, who cannot be identified, has severe cerebral palsy after being starved of oxygen to the brain when she was born at the Ulster Hospital.
Her family sued the South Eastern Health and Social Care Trust for alleged medical negligence.
Following a lengthy legal battle, it was confirmed at the High Court in Belfast that liability was not to be contested.
The pay-out confirmed as part of the settlement reached is believed to be one of the biggest of its kind in Northern Ireland.
Lawyers representing the girl brought a claim over the procedures and actions during her birth in 2008.
Because of her condition she now has a limited life expectancy, they confirmed.
A package of care arrangements had to be approved by the court before the case was finally resolved.
That will include a lump-sum payment and further periodical instalments for the rest of her life.
According to the family’s solicitor, Matthew Fitzpatrick of the Robert Sinclair law firm, the total level of damages is expected to top £5m.
Mr Fitzpatrick insisted the money will ensure their daughter receives proper care.
“This isn’t a lottery win for the family, it’s very small recompense for what they have gone through,” he said.
“They were failed at the birth of their child, and this has had massive repercussions on the wider family circle.”
Mr Fitzpatrick also disclosed how his firm had used modern techniques in the case.
“We obtained a video diary of the everyday difficulties the family faced, and this has helped in keeping their stress to a minimum,” he added.
“Before evidence was finalised we also took a proactive approach in securing an interim payment of £500,000 to assist in this girl’s immediate needs and relieve some of the family’s stress.”