The High Court heard the boy was brain damaged when he was born at Blackpool Victoria Hospital in Lancashire.
The family’s barrister told the court the boy’s father, who cares for him full time, could not afford the train fare to attend the proceedings.
The hospital trust has apologised to the boy’s family.
Judge Mrs Justice Lambert said the boy suffered from acute mental and physical disabilities and is cared for at home by his father.
The settlement means the boy, who cannot be identified for legal reasons, will get professional care for life.
He will receive a £5.7m lump sum, plus inflation linked and tax free payments each year to cover the costs of his care for life.