The child, who cannot be identified, developed severe cerebral palsy after being starved of oxygen to the brain when he was born at Altnagelvin Hospital.
The pay out confirmed as part of a settlement reached in the case is believed to be one of the biggest of its kind in the North of Ireland.
Lawyers representing the boy’s family sued the Western Health and Social Care Trust for alleged medical negligence.
The claim centred on procedures and actions during his birth in 2012.
He sustained a traumatic brain injury which left him with profound disabilities.
Liability was accepted days before the action was due to go to trial at the High Court in Belfast.
Negotiations then centred on the level of damages to be awarded to cover the care and specialist therapies the boy will require for the rest of his life.
The settlement, approved today, Wednesday, January 16, by Mr Justice Maguire, is expected to reach £4.9m.
Solicitor Harry McAleese of McCartan Turkington Breen, who represented the child, said outside court: “The family are delighted and relieved at the outcome of this long-running case.
“This settlement will enable them to provide the necessary support and comfort for their child.”
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