The Met police said two officers on marked police motorbikes saw a motorcycle with two males on it running a red light on Oxford Street.
They pursued the motorbike into Tottenham Court Road where it was in collision with a taxi and street furniture, the Met said.
A boy, 18, who was rising the moped, died at the scene despite efforts of the emergency services to save him.
A 17-year-old who was riding pillion suffered non life-threatening injuries to his arms and legs and was taken to hospital.
The Met Police said he was found in posession of a machete and arrested.
The two police motorcycles believed to have been involved in the incident were being examined at the scene on Monday.
The wreckage of the scooter, which collided with a taxi, lay next to the police bikes.
The police watchdog the Independent Office for Police Conduct (IOPC) has launched an investigation.
The Met’s Directorate of Professional Standards (DPS) has also launched an investigation alongside the Met’s Roads and Transport Policing Command.
Hospital workers from University College Hospital which is next to the scene of the crash scene raced out to help the victims.
A witness said: “Hospital workers ran out to help after there was a big crash sound. They were in the scene quickly. They were heroes.”
A builder said: “I was on the way to site when I heard a bang and scaling metal. People were running to help, they looked like hospital workers.”
A local shopkeeper said a relative of one of the boys was seen in tears at the scene later on Monday.
A spokesperson for police watchdog the Independent Office for Police Conduct (IOPC) spokesman said: “We can confirm we have begun an independent investigation into the circumstances of a fatal road collision involving a motorcycle in central London this morning (Monday).
“We understand the collision took place at around 6.45am after the motorcycle had failed to stop for two marked Metropolitan Police Service (MPS) motorbikes in Tottenham Court Road.
“Shortly afterwards, the driver of the motorcycle, aged 18, is understood to have been in collision with a taxi and sadly died at the scene. A pillion passenger, aged 17, sustained non-life threatening injuries.
“After being notified by the MPS, we have sent investigators to the scene and to the police post incident procedure to begin our enquiries.
“Our thoughts are with all those affected by this tragic incident.”
A section of Tottenham Court Road remained behind a police cordon on Monday afternoon.
The disruption cause huge traffic congestion in the area around Tottenham Court Road and Euston Road.