Stefan Appleton, 18, was with friends when he was attacked in Nightingale Park in Islington on 10 June last year.
The killer stabbed him with the 25in (63cm) serrated blade after leaping off a stolen moped, the Old Bailey heard.
The 17-year-old, who cannot be named due to his age, was cleared of murder. He will be sentenced on 21 April.
Mr Appleton, a college student from Islington, had been with friends when his attacker jumped off the back of a scooter, pulled out the weapon and chased after the victim and his friends, the jury heard.
He was stabbed repeatedly after tripping and falling. The cause of his death was shock and haemorrhage due to a stab wound to the chest, police said.
The Metropolitan Police has issued guidance about 'zombie' knives, advising that this is how certain ornate knives are currently being marketed. The force says:
Children were playing in the park at the time of the attack.
As the killer was ridden from the scene, the court heard he shouted out "RP" - standing for Red Pitch, a rival to a gang in the Nightingale Park area.
The alleged getaway rider, 17, was cleared of murder while another boy, also 17, was found not guilty of conspiracy to cause grievous bodily harm.
After the machete attack, the killer fled to Bristol and tried to fly to Malaga in Spain, but was arrested when he returned to London to lie low.
In his defence, the killer said he had come under attack when he went to snatch back his bicycle which had been stolen by another boy.
The court heard he had a previous conviction for possessing a blade after being caught with a lock-knife in a McDonald's restaurant a year before the killing.
Prosecutor Simon Denison QC said Mr Appleton's death was another "tragic waste of a young life" taken by a knife.
Speaking after the conviction, Det Ch Insp Chris Jones said: "There can be absolutely no excuse for young people to carry such dreadful weapons on London's streets and this case once again highlights the awful consequences of doing so."
A boy has been found guilty of the manslaughter of a teenager he stabbed with a "Zombie Killer" machete in north London.