The nine-year-old's family sought redress from NHS England and South Central Ambulance Service after he became unwell in 2007 aged six weeks.
He received treatment at the Royal Berkshire Hospital, but it came too late to prevent injury to his brain.
The organisations denied liability, but agreed to settle the case.
The High Court heard that the child, who is from Berkshire but who cannot be identified, requires around-the-clock care.
He has severe cerebral palsy, profound learning disabilities, deafness, severe visual impairment and epilepsy.
His legal team alleged his condition was the result of negligence by two GPs and a paramedic.
They argued the boy would not have suffered the injuries if he had been given antibiotics and hospital treatment sooner.
Mr Justice Kerr said the payout, which will be used to provide the boy with life-long care, "marks the end of a long and difficult process".
He will receive a £2.3m lump sum and index-linked annual payments of £237,660 which will increase to £259,257 when he turns 19.
Speaking after the hearing, the family's solicitor, Olivia Scates, described the case as "extremely tragic and distressing".
"His family have been devastated," she said.
"I am delighted the family will now have access to the help they need to provide for his extremely severe disabilities."
A boy who suffered "catastrophic brain damage" after contracting meningitis as a baby is to receive £4.6m in compensation from the NHS.