Four charges against him were dropped by the Crown Prosecution Service (CPS) on Tuesday “following a review of the evidence”.
They related to the former West Yorkshire Police chief inspector telling alleged lies about his involvement in the aftermath of Hillsborough and the culpability of fans.
Ninety-six people died in a crush at the Sheffield Wednesday stadium on April 15 1989 before an FA Cup semi-final.
An inquest jury ruled in 2016 they were unlawfully killed.
Sir Norman, 62, was at the game but was off duty, attending as a spectator.
In the aftermath of the tragedy, he was tasked with finding material for police lawyers to present to the public inquiry, led by Lord Justice Taylor.
He later applied for the job of chief constable in Merseyside – an appointment that caused controversy when it emerged he had not mentioned his work on Hillsborough in the application form.
The four charges included an accusation Sir Norman untruthfully described his role in the response as “peripheral” and the claim he lied about never having having tried to shift blame for the disaster “on to the shoulders of Liverpool supporters”.
He was accused of two further claims of claiming he never “besmirched” Liverpool fans and never offering any interpretation other than that the behaviour of Liverpool fans did not cause the disaster.
Explaining the decision to stop criminal proceedings against him, CPS director of legal services Sue Hemming said there had been “significant developments which have affected the available evidence” since he was charged in June 2017.
Two witnesses had changed their evidence and a third had died, she added.
“Our latest review of the evidence has concluded the collective impact of these developments means there is no longer a realistic prospect of conviction,” Ms Hemming said.
“I appreciate this news will be disappointing for the families and the CPS will meet with them in person to explain the decision.”
Five other men, including Hillsborough match commander David Duckenfield, are due to face trial for offences related to the disaster next year.
Due to the ongoing cases, Ms Hemming said it was “extremely important that there should be no reporting, commentary or sharing of information which could in any way prejudice those proceedings”.