Eyjolfur Andrews, 16, was also given concurrent sentences after pleading guilty to that armed robbery in February and to another armed raid six weeks earlier when he stole pounds 650 worth of cannabis from a drug dealer's home.
The first sentence was imposed for the murder of Amaranath Bandaratilleka, 32, a barrister's clerk known as Nath Banda, who was blasted by a shotgun at close range in the shop in King Street, Hammersmith, west London.
Andrews, of Hammersmith, had pleaded guilty to Mr Banda's manslaughter but the jury convicted him of murder.
Judge Geoffrey Grigson also gave him three years for possession of a single-barrelled sawn-off shotgun, six years for the earlier robbery, in Uxbridge, west London, and eight years for the second.
Sam Perman, 18, of Hammersmith, who was with Andrews on the King Street raid, will be sentenced later. He was found guilty of that robbery, possession of a firearm and of manslaughter.
The judge said Andrews had been described as a personable young man of average intelligence who was in some respects mature above his years and normal in manner and behaviour.
He told him: 'It is a tragic irony that had you not filled yourself with drugs you would have been something like that in January and February this year. Instead, you were violent and dangerous and a menace to yourself and others.
'You killed Mr Banda and brought sorrow and distress to his family and yourself and you ruined your own life and the life of your friend Sam Perman.'
The boy's father, Barry Andrews, was in court when his son was sentenced. He refused to comment. Mr Andrews, who has appeared in the ITV series The Bill, persuaded his son to give himself up to police. Andrews told his father that the gun went off by accident.