Sorrell Leczkowski, from Adel, was among 22 people who died when a suicide bomber attacked concertgoers on Monday.
Her mother and grandmother were also injured in the attack and are both being treated in hospital.
In a statement issued on behalf of the family by Greater Manchester Police, Michael Healey described his granddaughter as "our rock".
He said she was a "clever, talented, creative girl" who dreamed of becoming an architect.
She had planned to go to Columbia University in New York to study "so that she could build hotels with slides coming out of the rooms and so that she could build her mum a house".
Mr Healey said his wife Pauline remains in intensive care and Sorrell's mother Samantha is recovering from surgery "as she tries to make sense of the devastating loss of her daughter".
The BBC understands Sorrell and her mother and grandmother were not at the Ariana Grande concert but had gone to collect her sister who was not injured.
Sorrell was a year nine student at Allerton High School.
In a letter to parents informing them of Sorrell's death, head teacher Elaine Silson said she was "deeply saddened" by the news.
"Sorrell was a delightful member of the school community. She enjoyed her studies, had a lovely group of friends and was a real asset to Allerton High School," she said.
"Our whole school community is extremely shocked and saddened by this and our thoughts are with Sorrell's family and friends at this very difficult time."
She said staff and students were being supported by Leeds City Council, West Yorkshire Police and other external agencies.
Liberal Democrat candidate for Leeds North West Greg Mulholland tweeted to say: "My condolences thoughts and prayers are with the family of 14-year-old Sorrell Leczkowski from Adel, Leeds, a victim of the Manchester attack."
He said he had attended vigils in Leeds and Otley on Tuesday to remember the victims and those still missing.
"It is heartbreaking that amongst the victims is a 14-year-old girl from Adel," he said.
"My thoughts and prayers go out to her family and to the families of Wendy Fawell [from Otley] and [Leeds Beckett University student] Courtney Boyle, who are also missing and to the three local women who are receiving treatment for serious injuries."
Two online fundraising campaigns have been set up to raise money for Sorrell's mother and grandmother.
Since the pages were set up on Wednesday a combined total of more than Â£8,000 has been raised.

The man in his 30s was found with serious head injuries in Haig Avenue, Chatham at about 22.55 BST on Tuesday.
Police believe he was attacked during a disturbance in Glencoe Road and Magpie Hall Road, minutes earlier.
A 26-year-old local man arrested on suspicion of attempted murder remains in custody.
Kent Police have also held a 27-year-old woman, also from the town, on suspicion of assisting an offender.
Det Insp Ivan Beasley said: "The victim remains in a very serious condition in hospital with life-threatening injuries."
A 14-year-old girl from Leeds has been named as a victim of the Manchester Arena bomb attack.
[NEXT_CONCEPT]
A man has been arrested on suspicion of attempted murder after a man was critically injured in a "disturbance" involving several people.