Mark Duggan was probably throwing a handgun away when he was shot by officers, the police watchdog has said.
He was under Metropolitan Police surveillance when he was shot in Tottenham on 4 August 2011, sparking England-wide riots.
The Independent Police Complaints Commission (IPCC) found the operation targeting Mr Duggan was "appropriate".
Its three-and-a-half-year investigation cleared the Metropolitan Police of any wrongdoing.
'Chronicle of incompetence'
The Duggan family released a statement in which they claimed the report "confirms their belief that the IPCC are unfit for purpose".
The family described the watchdog's conduct as "a chronicle of inefficiency and incompetence".
They criticised the investigation for being "far from robust about a number of matters" and called on the IPCC to produce a "supplementary report" to address a number of their concerns.
According to the IPCC's report, the "most plausible explanation" was that Mr Duggan was in the process of throwing the weapon away when a police officer fired two shots at him.
Officers had attempted to inform Mr Duggan he was required to stop, it said, but without supporting radio or video recordings it was impossible to know whether they had shouted "armed police" or not.
The IPCC said it was "surprising" none of the police saw the gun leaving Mr Duggan's hand but it had found "no credible evidence" to suggest the weapon was planted.
Its report recommended in-car video recordings were made of any future covert operations, and retained for use by the IPCC in the event of death or injury.
All radio communications during covert firearms operations should also be recorded, it said.
Without such material in Mr Duggan's case, it said, it was impossible to know exactly what had happened.
The gun was given to Mr Duggan by Kevin Hutchinson-Foster, who had used it six days earlier to pistol whip a man during a fight.
Two detectives are now facing misconduct proceedings over allegations they failed to investigate the assault "promptly".
But the IPCC said even if police had responded more quickly it was "highly unlikely" the gun would have been seized before it was passed to Mr Duggan.
Deputy chairwoman Rachel Cerfontyne said the recommendations would shorten investigations and provide "immediate, accurate and incontrovertible evidence".
Responding to the report, Met Police assistant commissioner Patricia Gallan said it was important to note the IPCC had found no wrongdoing or misconduct by any armed officer involved in the operation.
She urged people to study the report, based on 1,200 documents, 500 witness statements and 340 exhibits.
Ms Gallan said she hoped the report would help people make sense of the events on the day.
Police and other agencies now have 56 days to respond to the IPCC's recommendations.
Last year, an inquest jury found Mr Duggan had been lawfully killed - but did not have a gun in his hand when he was shot in Ferry Lane.
The firearm was found behind railings in a grassed area about 14ft (4.2m) away.