The 69-year-old actor was arrested in April, accused of beating his wife Elaine and daughter Lizzie "during a boozy late-night family row" at their Essex penthouse.
However, The Mirror reports that the Crown Prosecution Service has said that no further action will be taken.
A spokesman confirmed: "We can confirm that the case has been discontinued and no further action will be taken."
Murray, who also appears in advertisements for Injury Lawyers 4 U, had apparently put his career on hold following the arrest.
The London-born actor appeared as gangster Johnny Allen in EastEnders from January 2005 to October 2006. He had previously starred in axed ITV police drama The Bill as the corrupt DS Don Beech.
> Billy Murray: 'I miss EastEnders'