The crash occurred when another car on the wrong side of the road collided with the car in which the child was travelling with her mother and friends.
Ms Arendse, of Mullagh, Kells, Co Meath, who was a back-seat passenger wearing her seat belt, suffered severe injuries in the accident which occurred on the Julianstown to Duleek Road on June 28, 2009.
Yesterday, Alexander Owens, for the child, told Mr Justice Kevin Cross the case had settled for €3.9m.
Through her mother, Bridgitte Arendse, the child had sued the driver of the other car -- Sean McKenna, Drogheda Road, Duleek, Co Meath -- and its owner, Patricia McKenna, of the same address.
It was claimed Mr McKenna was driving on the wrong side of the road as he approached the car in which Ms Arendse was travelling.
Counsel said his client suffered spinal injuries, is now paralysed from the waist down and had also suffered severe abdominal injuries.
Mr Owens said liability was never an issue in the case.
While Ms Arendse lost a year of school, she is now coping well with her studies, counsel added.
Approving the settlement, Mr Justice Kevin Cross congratulated the legal teams for an "excellent" settlement and said he hoped Ms Arendse manages to build a great life for herself and he was sure she would.
The Arendse family moved to Ireland from South Africa several years ago.
Before the accident, Ms Arendse was a very sporty girl and loved to swim, the court heard.
The local community had also raised several thousands euro to help the family after the accident.