Robbie Crane had an operation on his heart when he was just days old, but alleged negligent post-operative care at Harefield Hospital in Middlesex in 1999 left him with cerebral palsy and no sense of fear.
Robbie needs 24-hour care as a result of what his lawyers claim was negligent treatment during a period of ventilation after his surgery.
A judge at the High Court heard that a settlement in the case had been reached with the Royal Brompton and Harefield NHS Trust, which denies liability.
Neil Block QC, for the trust, told the court that "notwithstanding that there is no admission of liability", the trust acknowledged that "serious issues" had been raised about Robbie's treatment. He apologised to Robbie's mum and dad, saying it was a "matter of profound regret".
Robbie will receive 70 per cent of the full sum, which is yet to be assessed, which is deemed necessary to give him the care, accommodation and support he will need for the rest of his life.
Robbie's parents, Catherine and Barrie, were praised in court by Mr Justice Owen for the devoted care they had given their son.
In a statement, Mr and Mrs Crane said:
"We almost can't believe that we've actually won this compensation for Robbie as we were told on a number of occasions that we stood no chance.
"We have always provided Robbie with constant loving care and this award means that he will still be cared for when we are no longer able to do so."