The victim was named by his mother as Rhyhiem Ainsworth Barton.
He was discovered with critical injuries on Warham Street in Southwark on Saturday evening.
Scotland Yard said officers were called to reports of gunshots on nearby Cooks Road at about 6.05pm.
Paramedics from the London Ambulance Service and London’s Air Ambulance went to the scene, but the teenager was pronounced dead just before 7pm.
Rhyhiem’s mother, Pretana Morgan, told reporters near her home in the Brandon Estate: “I couldn’t have asked for a better son.
“My son was a very handsome boy. He’s got so much potential.”
Ms Morgan said Rhyhiem was “trying to make a difference” by learning to work with children.
“This is not life. My son’s a good boy,” she added.
Police tape surrounded much of the area around Aberfeldy House and officers remained at the scene on Sunday morning.
St John the Divine Primary School is just outside the police cordon.
Ms Morgan criticised police, saying: “We’re not being protected because of the police.
“The police are the ones putting us in danger.”
Metropolitan Police have urged anyone who was in the area of Aberfeldy House at the time of the shooting to contact them.
The death is the latest in a spate of violent crimes in the capital, as police investigate more than 60 alleged murders so far this year.
Police have yet to formally identify the victim and a post-mortem examination will take place in due course.
No arrests have been made.