The 17-year-old from Barnsley in South Yorkshire, who was on The Smiler with her boyfriend Joe Pugh, also suffered a fractured left hand.
The announcement came on the day the amusement park in Staffordshire reopened for the first time since Tuesday’s crash, in which two carriages on the rollercoaster collided.
Two others suffered serious injuries, while another 12 were hurt.
One of the four badly hurt in the crash, Victoria Balch, had surgery for “significant lower limb injuries” on Saturday, which was her 20th birthday.
Daniel Thorpe, a hotel assistant manager from Derbyshire, suffered a collapsed lung and a fractured leg in the accident, according to his father.
In a statement, Leah’s father David said: “Leah has suffered a life-changing injury and now has many months of rehabilitation ahead of her.
“We have done this to put people’s minds at rest and we would also ask everyone to respect Leah’s privacy as she undergoes this rehabilitation.
“We would like to thank all the emergency services at the scene and all the hospital staff who saved Leah’s life.”
Joe’s father Simon said: “I would like to thank our friends and family for their support.
“We would also like to thank the staff at the hospital who have been very accommodating, have been lovely to us and have protected our privacy.
“We would ask people to respect Joe’s privacy now and over the weeks and months ahead.”
Nick Varney, the chief executive of Merlin Entertainments, said of the reopening: “We are very aware of the impact it will have on those involved and we are doing all we can to provide our support to those injured and their families.”
Despite the resort opening its gates, the area where The Smiler is located – known as the X-Sector – will be cordoned off until the Health and Safety Executive has concluded its investigation.
A prohibition notice was placed on the rollercoaster by officials, forbidding its reopening until action has been taken to address the cause of the collision.
It is estimated that Merlin Entertainments, the company which owns Alton Towers, may have lost as much as £3m in revenue during the closure, or £500,000 a day.
Another Alton Towers rollercoaster, The Spinball, will be closed until further notice while enhanced safety measures are put into place.
A spokesman said this was taking longer than usual because of the ride’s design.
Other rides at Thorpe Park and Chessington World of Adventures also remain out of service, but are expected to reopen soon.