Mark Duggan, 29, did not have a gun in his hand at the time of the killing in Tottenham, north London, in August 2011, the jury at the Old Bailey court found.
But the father-of-four did have a gun with him when police stopped the taxi in which he was travelling and he threw it away shortly before he was shot, they said.
After the jury recorded a verdict of lawful killing by a majority of 8-2, Duggan's brother shouted obscenities at jurors as they left court while other supporters screamed "murderers."
Inquests are heard in Britain after sudden or unexplained deaths.
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The jury had a choice of three conclusions: lawfully killed, unlawfully killed and an open conclusion.
Two days after Duggan was killed, the deprived district of Tottenham erupted in violence, and the unrest then spread across the capital and on to Birmingham, Manchester and other English cities.
Five people were killed and dozens injured in the violence while millions of pounds' worth of property was damaged or destroyed.