Ayla Ellison, of Ulverston, Cumbria, suffered severe brain damage following a "traumatic" birth at Furness General Hospital, Barrow, in April 2007.
In 2012, Morecambe Bay NHS Foundation Trust admitted staff negligence.
At London's High Court earlier it was ruled the trust will pay a tax-free sum every year for the rest of Ayla's life.
Mr Justice Warby ruled the organisation must pay an index-linked amount starting at £225,000 and rising to £290,000 when she turns 18.
While admitting it was at fault, the trust had disputed the value of the claim for damages. It has been providing financial assistance to the family since 2012.
Ayla, now eight, is totally immobile and dependent on being fed through a tube.
The court was told she is at constant risk of hypothermia as she cannot control her body temperature.
Despite her immobility, she suffers muscle spasms that leave her "screaming inconsolably at the top of her voice for hours".
Painkillers do not stop the pain, which can only be quelled by immersion in a hydrotherapy pool.
Ayla's father now works in London and the settlement includes £1.6m to buy a family home in Richmond. Further money will be needed to adapt it to Ayla's needs and install a hydrotherapy pool.
The judge awarded a £295,000 lump sum for Ayla's pain, suffering and disability and he paid tribute to her parents for the "calm and intelligent way" they had dealt with the tragedy.
Trust medical director David Walker said: "We are very sorry for the harm caused to Ayla and the distress caused to her family as a result of the issues arising from her birth.
"The injuries she suffered are very severe and a tragedy for her and her family. Her parents have had to cope with extraordinary pressures in looking after her."

Lincolnshire Partnership NHS Foundation Trust was criticised by the Care Quality Commission (CQC) in March 2015.
A re-inspection in April this year found it had made "positive progress" in some areas, but improvements were still needed.
The safety of patients at high risk of suicide had been deemed inadequate but has now been improved.
The trust currently has about 27,000 patients across the county and more than 2,000 members of staff.
Dr Paul Lelliott, deputy chief inspector of hospitals for the CQC, said there was now "good care" for the population served by the trust.
"We saw staff treating patients with kindness, dignity and respect," he said.
The use of volunteers and therapy dogs was praised, as was the patient-run cafÃ© and the range of paid job opportunities, including gardening and car valeting.
In March 2015 patients at risk of suicide were found not to be kept safe, but the trust said it now monitors "ligature risks", which are fixed points which someone could use to harm themselves.
"Heat maps" are also used to show patients at high risk of suicide.
Dr John Brewin, trust chief executive, said: "I am pleased that the work of all of our staff has been reflected.
"Our staff have a real focus on providing high-quality care for our patients and this latest report is testament to that commitment."
Improvements are needed in the areas of care plans, staff supervision, bed availability and delays in patients accessing psychological therapies, the CQC said.
The trust was also found to have good relationships with the community and police.

Ex-Leeds prop Bailey, 31, joined after the start of the season and made 15 appearances for Wire.
Forward Cox, 24, arrived on a one-year deal from Hull KR while Australian prop Dodds, 27, had an injury-hit season.
"I'd like to thank all three players for their contributions over the season," said head coach Tony Smith.
A girl left disabled after being starved of oxygen at birth has been awarded a multimillion-pound compensation package.
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An NHS mental health services provider has been upgraded from "inadequate" to "good" following a recent inspection.
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Super League side Warrington Wolves have announced Ryan Bailey, Jordan Cox and Mitchell Dodds will leave at the end of their contracts.