Police said they did not believe the incident was terrorism-related and there was no ongoing threat to the wider community.
Police tasered and arrested the man after the incident near Hainault in east London.
Video footage obtained by the PA news agency showed a man wielding what appeared to be a sword.
It shows how officers shout at the suspect, saying "Don't move, don't f***ing move," after he is brought to the ground by three separate Taser discharges.
Footage then shows seven officers swarm around the suspect, with three brandishing truncheons and the two officers with Tasers still pointing them at him.
The words "Suspect contained" are then heard as a female officer pulls the sword away from the man.
The suspect is then told "You are under arrest for murder" just over a minute after officers attempted to apprehend him.
"It is with great sadness that I confirm one of those injured, a 14-year-old boy, has died. He was taken to hospital after being stabbed and sadly died shortly afterwards," London's Metropolitan Police Chief Superintendent Stuart Bell said.
He said it was not believed to be a targeted attack.
Initially, police had said the victim was a 13-year-old.
London's Metropolitan Police Assistant Commissioner Louisa Rolfe told reporters a 36-year-old man had been arrested on suspicion of murder and was currently in hospital, having suffered injuries when his van collided with a building.
Two members of the public and two police officers were in hospital with non-life threatening injuries.
The two police officers had stab wounds requiring surgery.
King Charles paid tribute to those affected and praised the courage of the emergencies services that helped to contain the incident.
"His (King Charles) thoughts and prayers are with all those affected - in particular, the family of the young victim who has lost his life," a Buckingham Palace representative said.
with PA
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