Kieron Smith, 18, murdered 10-year-old Lauren Pilkington-Smith in Leigh, Greater Manchester, on July 7.
She went missing after playing cricket with Smith and a younger boy near their homes.
Her body was found later that night in local woods by her grandfather after the family launched a frantic search when she failed to return home.
Smith was found guilty by a unanimous verdict following a Liverpool Crown Court trial lasting nearly two weeks.
Mr Justice Mackay adjourned sentencing for reports but said: "There is only one sentence that can be passed on him and that is a life sentence."
Jobless Smith, who left school at 13, admitted playing cricket with Lauren but always insisted he had gone home afterwards and not seen her again.
Television
He told police and the jury that he spent the evening watching television, playing computer games, cooking his tea and taking the family dog for a short walk.
But evidence from witnesses and other sources proved that Smith's story did not add up.
He was also unable to explain how tiny droplets of Lauren's blood came to be on his trainers.
His reason for killing Lauren, described in court as a "popular and well mannered" girl, may never be known.
Smith had been told he suffered from Asperger's Syndrome, a form of autism, but that illness was not presented as a defence by his legal team.
Lauren’s parents were in court to hear the verdict but were too upset to talk afterwards.
Lauren’s grandmother Pat Smith read out a family statement in which she described the loss caused by the murder.
She said: “Lauren had a wonderful sense of humour, she always had a smile on her face.
“Lauren was very keen on all sports and we used to go as a family to watch her on school sports day. The only outing we have now is to the cemetery.
“Kieron Smith has deprived Lauren of life. We will never know what the future would have held for Lauren. She may have been a great athlete. Who knows, but at least she would have had a future.
“We have been deprived of seeing Lauren grow up into a sensitive, caring adult, which she was as a child.
“Lauren’s death has destroyed us. We get up in the morning thinking about Lauren and we go to bed at night thinking about Lauren. Our lives and our home will never be the same again.”
Ken Pilkington, Lauren’s grandfather, discovered her body on the night of the murder.
He said outside court: “At least the jury has had the common sense to put this fellow away for good.
“Hearing what happened in court has been terrible. We didn’t know the full extent of the injuries. We are devastated.”

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Pleased to hear justice has been done for Lauren and her family/friends.
Hopefully the killer won't be allowed out ever again.
R.I.P Lauren.
Hopefully after this gulity verdict Lauren's family and friends can carry on with their lives and remember her for the wonderful girl she was.
I am so glad justice has been done!!!
My heart goes out to Laurens family at this time and I hope they know the community is with them and thinking of them.
Justice has been done.
All my thoughts are with Lauren's family at this time as nothing will ease the pain of their little girl's death.
R.I.P Lauren
Another candidate for the gallows. But alas Tony Blair and his cronies will not support it
I hope they mean life when they say it - would hate to think that he might be out in 15 years to make a new life for himself and probably with government help, the perpetrators get a very good deal here, its the victims that keep suffering.
And yet another rat we have bred?
When will this looney liberalised system of ours change ? When are we going to get our children back under control how many more innocent children have to die because we have a weak government and system .Bring back corporal punishment and hanging back only then will we get control back in britain. My sympathies got out to the girls family but while this monster is still alive in prison they will never have peace?They will always live in fear that this monster will be released early??
i realy think its high time we had a referendum on wether to bring back hanging ,it will cost the taxpayer millions to keep this creep in clink in a life of luxury .games room ,colour tv ,video games ,cordon blau food ,i think it should be in the torys election manifesto .
Let's hope that this fiend gets what is coming to him when he's inside. If the world was straight, he'd be frying on the chair by now. How much longer do we have to put up with vermin like this taking the lives of innocent kiddies?
R.I.P Lauren u liv eon in everyones memory, glad justice has been done if only all the people whop have done thi could be caught then the world will be a better place my regard go out to the family!