Kevin Hutchinson-Foster was found guilty at the Old Bailey of giving Mr Duggan the gun just 15 minutes before he was shot dead on August 4, 2011.
The 29-year-old's death in Ferry Lane, Tottenham, north London, sparked riots that swept across London and other English towns and cities.
Hutchinson-Foster, 30, who is already in prison for drugs offences and was on licence at the time he gave Mr Duggan the gun, had already pled guilty to using the same gun to threaten people in a barber's shop just six days before, as well as using it to "pistol whip" a barber.
He is seen on CCTV threatening Peter Osadebay then returning and beating him with the gun until he nearly lost consciousness.
Hutchinson-Foster pled guilty to possessing a firearm with intent to cause fear of violence and assault occasioning actual bodily harm.
He denied selling or transferring a prohibited firearm to Mr Duggan between July 28 and August 5, 2011, and a jury failed to reach a verdict in an original trial, prompting a retrial at the Old Bailey which led to his conviction.
He will be sentenced on February 26.
The court heard Mr Duggan, who was under police surveillance that day and the day before, had gone in the minicab to Leyton, east London, where he collected the BBM Bruni Model 92 handgun in a shoebox from Hutchinson-Foster, before continuing to Tottenham.
The cab was pulled over by armed police in four unmarked cars in a "hard stop", and as Mr Duggan got out holding the gun, he was shot by CO19 officers.