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The victims' families said the decision by John Larkin was an important step in their ongoing campaign for justice.
The Army said it opened fire in response to gunfire from republican paramilitaries.
The families have carried out a long-running campaign for an independent inquiry into the killings.
Ten people were shot dead during the shootings and another man died from what the families claim was a related incident.
John Teggart - who's father Daniel was killed - said the original inquests were flawed.
"The evidence of these soldiers was in crafted statements handed to the judge," he said.
"You had witnesses who came to the inquest who weren't called, they weren't cross examined.
"That's what you had then but things have changed and we hope to get proper inquests into the deaths of these 10 victims."
SDLP West Belfast MLA Alex Attwood said Mr Larkin's decision underlined the need for a full international inquiry into the atrocity.
"The decision by the attorney general on the Ballymurphy massacre is a step in the right direction. This decision vindicates the campaign of the families for truth and justice," he said.
"This development, however, serves to confirm that it is a public, international inquiry that is needed to give the families the means to truth that their campaign demands."
The 11 victims, which included a priest and a mother-of-eight, were killed in August 1971 by members of the Parachute Regiment during Operation Demetrius, when people suspected of paramilitary activity were interned.
The Northern Ireland Office has ruled out any public inquiry into the killings akin to the Bloody Sunday Tribunal.
The republicans won't stop now until they get the result they want.
Then it'll be finnucane enquiry, drumm enquiry etc.....
Nothing about Narrow Water La Mon Bloody Friday Darkley Ballykelly.......
Need I go on.... we all know what i'm on about.
Selective inquiries. Which party is going to have the balls to say ENOUGH.