The footage, by someone who says they witnessed the shooting, includes attempts to save Mr Duggan’s life following the incident last August.
On the tape, the witness recounts that Mr Duggan jumped out of a car and police twice shouted: “Put it down.”
The witness who provided the footage to the BBC has asked to remain anonymous.
Mr Duggan was shot by police on 4 August in north London. Within days there was rioting in Tottenham – the scene of the shooting – which then spread across England in the worst disorder in a generation.
The 29-year-old father-of-four was a passenger in a minicab when it was stopped in a planned operation involving the Metropolitan Police’s Operation Trident, which investigates gun crime affecting black communities, and officers from the specialist firearms team CO19.
Two shots were fired from a police gun and Mr Duggan died from a single gunshot wound to the chest. A non-police issue firearm was found at the scene.
The IPCC has been unable to interview any of the police officers present at Mark Duggan’s shooting
The pre-inquest review into the death heard earlier this year that that gun had no traces of Mr Duggan’s fingerprints, DNA or blood on it.
The footage handed to the BBC begins just minutes after the police opened fire at about 18:15 BST.
It shows the people-carrier minicab that Mr Duggan had been travelling in and three unmarked police cars used to halt the vehicle. Mr Duggan is lying on the pavement as attempts are made to resuscitate him.
Buses initially pass the scene before the police have had time to close roads.
As time goes on, paramedics can be seen continuing emergency treatment in vain. Firearms officers wearing baseball caps can be seen moving around the scene.
During the footage, the witness provides occasional commentary of what has happened – and also recounts the moments before the filming began.
The BBC asked an independent audio analyst, who has worked on major police investigations, to listen to a key part of the commentary which is difficult to hear amid background noise.
According to the expert, the witness says: “They blocked him in, they blocked him in. He jumped out… And then he’s taken out, shot him … because I heard them shout at him yeah, ‘put it down, put it down’.”