The Davis family said in a statement that they are grateful for the 17 years they had with their daughter.
"The grace, laughter and light she brought to this world will not be extinguished by her death; to the contrary, it will only get stronger," the statement said.
The family said they appreciated the outpouring of support from the community and thanked the efforts of law enforcement, school officials and medical staff.
The date for a public memorial to honor the teen would be announced later, the hospital's statement said.
Friends and well-wishers had posted prayers online and raised money to help pay for Claire Davis' medical care in days following the shooting. The Denver Foundation set up a fund for donations to the Davis family on Friday, the same day about 100 people gathered at a church near the school to pray for the teen.
Karl Pierson, 18, shot Davis, who just happened to be sitting nearby with a friend as Pierson, armed with a shotgun, ammunition strapped to his body, Molotov cocktails and a machete, entered the school and headed toward the library. Davis appeared to be a random target, Arapahoe County Sheriff Grayson Robinson has said.
Pierson likely intended to track down a librarian who had disciplined him, but Robinson said Pierson's arsenal suggested Pierson intended to hurt many others at the school just 8 miles from Columbine High School.
Pierson set off one of the incendiary devices and fired five shots before killing himself just one minute and 20 seconds after entering the building. He knew a sheriff's deputy assigned to the school was closing in, Robinson said at a news conference.
Senior Chris Davis, who is not related to Claire Davis, said she loved horses, had a lot of friends and always seemed happy. Chris Davis, whose locker is next to Claire's, helped organize a fundraising effort for her family.
Students held vigils for Davis after the shooting. Typical was a story told by classmate Maggie Hurlbut.
"One time I remember I was upset in the hallway, and she came up to me and she just it was like, 'Hey Maggie, I know we don't know each other well but are you doing OK?' And I told her yeah, and she was like, 'Anything you need, I'm here for you,'" Hurlbut said.
Pierson's original target was believed to be a librarian who coached the school's speech and debate team. Pierson was a skilled speaker and debater on the team. The librarian, whose name was not released, had disciplined the teen in September for reasons that haven't been disclosed. Robinson said Pierson had made some sort of threat against the librarian in September.
The librarian was able to escape the school unharmed, Robinson said.
Pierson legally purchased his shotgun at a local store a week before the shooting and bought the ammunition the day of the shooting. Anyone 18 and older is allowed to buy a shotgun in Colorado; only those over 21 can legally buy a handgun.