Police are on the scene alongside the London Ambulance Service. London's Air Ambulance is also present.
Emergency services were called just after 12:30pm today. The pedestrian, a woman believed to be in her 80s, has been pronounced dead at the scene.
The collision took place at the western end of New Kent Road, at the new surface-level crossing between the shopping centre and the Elephant & Castle pub.
The Elephant & Castle roundabout has been closed and remains shut now. Police warned there was "significant travel disruption" in the area.
Huge tailbacks are being reported on New Kent Road and Old Kent Road, as well as on the Newington Causeway.
Motorists are being urged to use alternative routes.
Elephant & Castle is currently part-way through a £25m overhaul, in part to make it safer for for pedestrians, cyclists and drivers.
There have been more than 80 collisions in the area since 2012.
More to follow...