Kelyan attended Newhaven School, a pupil referral unit and specialist school in Eltham.
Head teacher Jon Kelly said: “We are devastated at the tragic death of this funny, kind and ambitious young man.
“It comes at a time when he was working incredibly hard at school to build on the successes he had already achieved since joining us.”
Mr Kelly said his thoughts were with Kelyan’s family and friends at “this unimaginably difficult time”.
St Columba’s Catholic Boys’ School in Bexleyheath confirmed Kelyan attended the school in 2022.
Paul Drake, the chief operating officer of the academy trust that runs the school, said staff and pupils were “saddened” by his death.
“Our thoughts and prayers are with his family and friends at this difficult time,” he said.
“Our schools will provide support to any of the students who may be affected by this senseless violence.”
St Mary Magdalene Church in Woolwich plans to hold a vigil in Kelyan’s memory this evening.
Police, paramedics and the London Air Ambulance were called to the scene on Tuesday afternoon after the alert was raised by an officer on patrol.
Medics tried to treat the boy’s injuries, but he died soon afterwards.
A crime scene remains in place around the area as investigations continue.
