Sir Norman, aged 62, had been charged with four counts of misconduct in a public office, all relating to alleged lies he told following the disaster at the 1989 FA Cup semi-final, in which 96 Liverpool fans died.
He was off duty on the day but in the aftermath of the tragedy was part of a team tasked with finding material for police lawyers to present to the public inquiry led by Lord Justice Taylor.
He was charged with misconduct for allegedly telling lies about his role in the disaster in 1998, when he applied for the chief constable job at Merseyside Police, and in 2012, when the Hillsborough Independent Panel report was published.
Sir Norman's lawyer Paul Greaney QC claimed "political pressure" had been put on the investigation, carried out by the Independent Police Complaints Commission.
He added: "The decision that has been made today reflects a recognition that a trial would not result in Sir Norman being convicted of any offence.
"That is for the simple reason that the evidence would not support a conviction. And that, in turn, is for the simple reason that he is in fact innocent.
"In the decision they have announced today, they have maintained their independence, notwithstanding the naked political interference that recently disclosed documents demonstrates to have occurred."
Speaking outside court, Sir Norman said his involvement in events around Hillsborough had been "misrepresented", including in Parliament.
He said: "Six years ago, I was driven from the job that had been my vocation for 40 years, and some commentators, who didn't really know anything about me or the facts, rushed to judgment and predetermined my guilt."