The court was told that he knew his victim well.
His father and her mother lived together in an extended family and he was a frequent visitor to her house, Justice Graham Panckhurst said.
When considering the minimum period he must serve behind bars, the judge said "age, immaturity is undoubtedly a matter that I must seriously consider."
He said people that age had the capacity to be rehabilitated.
Crown prosecutor Andrew McRae said Kelekolio had shown "very little remorse".
"His true motivation behind the offending ... remains unknown."
Justice Panckhurst said Kelekolio was in a state of denial, no doubt because of the "enormity" of what he did.
There were gasps of "yes" from the packed public gallery when the sentence of 14 years, six months was handed down today.
Miss Solomona's mother Anuella Solomona gave an emotional victim impact statement which told of having a "broken heart".
"When this happened to my daughter, I felt numb, lost for words, and made me think I was to blame for this," she said.
"My heart is in pain. I can feel the anger in my kids."
She said she would rather stay in bed now sleeping, rather than staying awake and thinking about what happened.
Mrs Solomona now felt like she had to leave New Zealand to make a fresh start.
Sina's twin sister Loretta Solomona said her sister's slaying was something she and the Ashburton community would "never forget".
She is now raising Sina's 4-year-old daughter whose mum was killed by the youth the family "treated as a young brother".
"My heart is broken," she said, telling Kelekolio that she hoped one day he would apologise to Sina's daughter.
Defence counsel James Rapley said Kelekolio's age needed to be taken into account when considering how long he should serve behind bars.
He spoke of his school struggles, where he was immature and had low intellectual function. He was suspended from Ashburton College for disobedience and misconduct.
From a young age, he was smoking cannabis and drinking to excess, Mr Rapley said.
He still won't talk about what happened, he said. "We don't have any insight from him."
Outside court, Kelekolio's father declined to comment: "Not right now."
Mr Rapley said it was too early to say whether he would appeal.
He said it was difficult for the Kelekolio family "to know their son has been sentenced for murder".
"It's very upsetting for both families, but especially for the Solomona family. This is horrific, tragic event that will have long-lasting effects for many families."
Detective Senior Sergeant John Rae said the sentencing was welcomed by the Solomona family, "who can move on now".
"It's not going to solve the issue but at least they can feel a lot better about the whole thing," he said outside court.
"These people who commit murder are the greatest thieves of all."
Miss Solomona's daughter, who is living with a "very good, big, tight" family, will "miss her mother every day", Mr Rae said.
