The 48-year-old was shot in the back of the head with a sawn-off shotgun outside his Edinburgh flat last month.
Police in Scotland confirmed late on Monday a 28-year-old man had been charged in connection with the actor's death.
He is due to appear at Edinburgh Sheriff Court on Tuesday.
In a statement, police said: "He is also charged with the attempted murder of a 48-year-old man and the serious assault of a 22-year-old man in Pitcairn Grove on Wednesday, March 13.
"Members of the public are thanked for their assistance with both of these investigations."
In the earlier incident, the older man was left with serious head and arm injuries, while the younger man suffered a cut to his hand.
A burnt-out car was also discovered in nearby Oxgangs
Boxing gym boss and actor Bradley was shot while he chatted to a neighbour on Chester Street in Edinburgh's plush West End on April 17.
His long-term partner Emma and eight-year-old daughter Eva were inside the £500,000 basement flat at the time.
One shocked local described hearing a single gunshot and turning around to see Bradley falling down the steps towards his flat while a man ran away.
He rushed to help Bradley but the Edinburgh-born star was already dead.
His death stunned many in the city, where the ex-hardman helped run the Helping Hands anti-poverty champion.
In his youth, Bradley was a boxing champ and ex-Hibernian football hooligan, and once featured in Danny Dyer's Deadliest Men.
He moved into the security trade and was jailed for terrorising estate agents.
But he had turned his life around, moving into acting before appearing in the sequel to Danny Boyle's classic 1996 film Trainspotting, based on Irvine Welsh's book of the same name.
In the sequel T2, Bradley — no relation to Irvine — played gangland boss Doyle who owns seedy saunas in Edinburgh.
He landed the role after setting a Guinness World Record for sparring with 360 people — including director Danny Boyle.
