Vass was awaiting trial for the rape of Ms Clough when he killed her in 2010.
He has not faced the sexual assault charges, something the family of Ms Clough has described as “wrong”.
Writing ahead of the announcement in the Times, Mr Starmer said Ms Clough had shown “tremendous courage” in reporting to the police Vass’s alleged assaults against her.
The 26-year old Lancashire nurse was stabbed 71 times by Vass in the car park of Blackpool Victoria Hospital in July 2010.
Mr Starmer said the rape charges against Vass were effectively superseded after he admitted the murder of Ms Clough, and that if proven they would not lengthen the overall jail term that could be imposed.
“In Jane’s case, Vass pleaded guilty to murder, so the rape charges were left to lie on the file, which is neither an acquittal nor a conviction.
“Jane’s parents felt that this was wrong. She had wanted Vass tried for rape and her murder effectively denied her justice,” Mr Starmer said.
After meeting John and Penny Clough, Mr Starmer decided to consult on a change to the rules for England and Wales.
“In cases where an offence as serious as rape is alleged in the context of a subsequent murder, the Crown Prosecution Service (CPS) should persist with the rape charges… even if no extra penalty can realistically be imposed.”
He said leaving charges such as rape to lie on file will now become “the exception, not the rule”.
Jane Clough’s family described the news as a “big step forward”.
Her father, John Clough, said: “When Vass was convicted of murder the existing charges of rape were left on file and we felt that didn’t give Jane any justice whatsoever so the campaign was to try and get the concept of keeping the charges on file to be reviewed.
“We are very pleased Kier Starmer has listened to the argument and instigated these changes.”
The new guidance also says that prosecutors must consult families whenever a plea or conviction for murder is entered.
Mr Clough said they had only been told about the decision to lay charges on file shortly before it happened.
“They are not promising to do what the family requests but they will give more consideration to the family’s desires and we think it is a big step forward,” he said.