Two other pedestrians were also found suffering from injuries after the collision at Eltham Road, at the junction with Kidbrooke Park Road, on Tuesday.
A 40-year-old woman and an eight-year-old boy were taken to a south London hospital for treatment.
Police say they are still in hospital but their injuries are not believed to be life-threatening.
Despite the efforts of medical staff, the 14-year-old boy was pronounced dead at 4.35pm.
A 40-year-old man has been arrested on suspicion of causing death by dangerous driving and has been released under investigation.
Police are now calling for information about the incident, saying it is vital that they give the child’s family answers about what led to his death just “a few days before Christmas.”
The 14-year-old boy’s family have been informed and are being supported by specialist officers.
Anyone who witnessed the collision is asked to call the police on 101 quoting reference CAD 4357/21Dec.
Detective Inspector Lucie Card, leading the investigation said: “This is a tragic incident which has resulted in the death of a 14-year-old boy.
“Our investigation into what happened is well underway, but we need anyone who witnessed what happened to come forward and speak to us.
“Likewise, I would also ask any motorists in the area to review any dashcam footage that may have captured this collision.
“It is vital that with give this child’s family answers about what led to his death just a few days before Christmas.”
A Met Police spokesperson said: “Police were called at 15:33hrs on Tuesday, 21 December to Eltham Road at the junction with Kidbrooke Park Road, SE12 following reports of a van collision in collision with a bus stop.
“Officers, the London Ambulance Service, London’s Air Ambulance and London Fire Brigade attended.