The girl, known as “A” for legal reasons, was a victim of extremely rare twin transfusion syndrome before her birth at Luton and Dunstable Hospital in 2001.
The condition meant that the “recipient twin” had increased circulation, at the expense of the “donor twin”, London’s High Court heard.
A’s twin died before birth, and A herself has been left blind, with severe physical and mental handicaps and a much shortened life expectancy.
Through her parents, A sued Luton and Dunstable Hospital NHS Foundation Trust, for damages. The family’s lawyers claimed medics were negligent in missing warning signs of the condition before her birth.
The Trust admitted full liability for what happened in 2008 and, through its barrister Judith Rogerson, apologised to the family in court on Thursday.
Mr Justice Foskett, approving a £6m settlement of the case, praised the “extraordinary devotion and care” given to A by her parents and siblings.
The payout is made up of £2.6m lump sum, plus annual, index-linked and tax-free payments to cover the costs of A’s care for life.
Those payments will start at £255,000-a-year, before rising to £300,000-a-year in 2020, the judge said.
He added that A is sadly not expected to live beyond the age of 30.
Fiona Neale, for the family, told the court that as a result of her in-utero injuries, A suffers from “full body cerebral palsy”.
She has serious learning disabilities and is also blind.
She has “no real appreciation of day or night” and so needs 24-hour care, the barrister added.
Praising the child’s family, she said they had given “over an above anything that would be normally expected. They have all pulled together.”
Miss Rogerson, on behalf of the trust, said: “I’d like to repeat the apology already offered to the family and say how sorry we are that there were these shortcomings in care.
“Although no amount of money can compensate for what has happened, we hope that this settlement can provide some comfort and security for the family and we wish them well in the future.”
Mr Justice Foskett, approving the settlement said: “All cases involving brain injury at the time of birth are sadly distressing and this is no exception.
“Here, the mother was carrying twins and suffered twin transfusion syndrome, a serious complication which means that one twin has an increased circulation at the expense of the other.
“Unfortunately the position was not identified and the donor twin died in utero, causing serious brain damage to the surviving twin.
“This claimant is totally dependant for care on a round the clock basis. Fortunately she has an immensely supportive family, which has and will continue to give extraordinary care. Her parents and siblings have given a huge amount of care.
“It is difficult to find words to describe the type of support she has received. In this case it is truly exceptional.
“This settlement will relieve the family of some extent of their enormous burden and ensure that A receives the support she needs and their will always be funds to meet her care requirements,” the judge concluded.