Quamari Serunkuma-Barnes, 15, was attacked as he left Capital City Academy in Willesden, north-west London, on 23 January.
Before he died in hospital, he managed to tell one of the nurses the name of his attacker.
The defendant, who cannot be named because of his age, had a string of convictions for violent behaviour.
He also had convictions for possessing a knife at school when he was aged 13.
Prosecutors at the Old Bailey described the murder as a "deliberate, planned attack on a defenceless schoolboy."
"He was happy and unconcerned as he walked out of the school gates, singing and exchanging banter with his school friends as he walked," said prosecutor Sally O'Neill QC.
But within three minutes of leaving school, he was chased and stabbed by a masked boy, dressed in black, who had been waiting for him at the corner.
Witnesses described Quamari shouting that he was going to be stabbed and "running for his life" back to the school.
He was unable to outrun the defendant who grabbed him and stabbed him three times in his back, shoulder and upper leg before running off.
One of the witnesses, a girl, recognised the attacker and almost immediately rang him. He lied to her saying he was in south London.
The masked figure was caught on CCTV waiting for Quamari to come out of school and his phone confirmed he was in the area at the time of the stabbing.
"This wasn't a school argument getting out of hand and someone getting hurt because one of them had a knife," continued the prosecutor.
"Whoever did this to Quamari Barnes was waiting for him and as soon as he saw him, he chased him, caught him and stabbed him three times."
The defendant refused to give evidence, but his barrister, Kirsty Brimelow QC, told the court that the case was "riddled with doubts" and that the police had simply "joined with the playground chat".
He will be sentenced on 28 July.
Det Ch Insp Jamie Stevenson said Quamari was a popular schoolboy who "didn't stand a chance" as his attacker was an adept runner.
"Many of the schoolchildren who witnessed the attack initially thought the two boys were messing around.
"Little did they know that within a matter of minutes Quamari would be lying helplessly on the ground fighting for his life. Those that witnessed the events have been left completely devastated by the loss of their friend."

If the team had to change the gearbox as a result of damage from Silverstone, Rosberg would be hit with a five-place grid penalty in Hungary this weekend.
Mercedes said Rosberg would run the gearbox in practice on Friday at the Hungaroring "to make sure it is OK".
A spokesman added: "We are optimistic that it will be."
Rosberg was demoted from second to third place at Silverstone after Mercedes were found to have broken rules restricting radio information given by teams to drivers as they tried to help him fix the problem.
The German heads into the weekend with a one-point championship lead over team-mate Lewis Hamilton.
Mercedes have not won the Hungarian Grand Prix since the start of their domination of F1 following the introduction of turbo hybrid engines in 2014.
Hamilton holds the record, jointly with Michael Schumacher, for most wins at the Hungaroring, with four victories.
Rosberg has never finished higher than fourth at the track.
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A 15-year-old boy has been found guilty of murdering a teenager outside his school gate.
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Mercedes say they are "optimistic" Nico Rosberg will avoid a grid penalty after the gearbox problem that afflicted him at the British Grand Prix.