Two men, thought to be in their late teens, were riding the vehicle when it collided with a van in Upper Clapton Road, Hackney, at 11:55 GMT.
The moped was linked to a suspected theft earlier. One rider died at the scene and the other is in a serious condition in hospital, police said.
The Metropolitan Police's professional standards directorate has been informed.
Officers said they were called at about 11:15 GMT to reports that a moped was spotted being driven away from Kingsland Road following a suspected theft.
The moped was sighted again about 30 minutes later in Stamford Road, police said.
When the driver of the moped failed to stop, a chase ensued.
The National Police Air Service was also called.
A teenage moped rider has died in a police chase in east London.