Garforth Academy pupil Amelia Wake was walking along a grass verge in Colton at around 4.45pm on Monday when she was knocked down.
The teenager from Rothwell was taken to hospital and died on Wednesday as a result of her serious injuries.
Today her family said they would treasure the time they had shared with her.
In a statement, they said: “Amelia was such a beautiful girl, both inside and out, she was so caring, kind and loved by everyone lucky enough to have her in their life. She was so special to so many people but none more so than us.
“Amelia was such a happy girl, always smiling, laughing and singing. We are devastated that her life has been cut short, at just 14-years-old she should have had her whole life ahead of her, but now we must treasure every single moment we shared with her.
“Amelia was doing so well at school and was very popular amongst her friends and teachers. We are so sad that her dreams and ambitions will never be fulfilled.”
They thanked all their family and friends for the support they had shown in what they described as “the most difficult time of our lives.”
The statement said: “We are drawing on their strength to help us through the loss of our daughter who was so tragically taken from us.
“We have been so proud watching her grow up and mature into an amazing young woman and words cannot begin to describe how much we love her and we will miss her so much.
“We are struggling to come to terms with the pain and sadness and why our precious daughter was taken. All we can think is Heaven must have chosen you for an angel.”
Police appealed earlier this week for any witnesses to the collision in Bullerthorpe Lane to come forward.
Detectives were particularly keen to speak to the driver of the car thought to have been travelling behind the blue Ford Focus involved.
Contact PC Tunney on 01924 293047 quoting log number 1042 of 30/05.