The court was told Sarah suffered cerebral palsy and is severely disabled as a result.
The legal action was launched when Ms Colhoun tried to get an explanation for her daughter’s condition, but was refused a meeting with medical staff.
An interim settlement was reached in the case and was approved by the High Court.
The case has been adjourned for three years, when it is hoped a statutory scheme will be in place to allow for further periodic payments.
Mr Justice Sean Ryan said it was a very good settlement for Sarah. He said while money would not solve the problems, the absence of it could make things a lot worse.
Afterwards, the family’s solicitor said they were pleased with the settlement, but disappointed it had taken so long for the HSE to admit liability.