The 45-year-old Lurgan man was seeking damages for alleged wrongful arrest, false imprisonment and malicious prosecution over the shootings in his hometown 16 years ago.
His claim against the RUC and British Attorney General was due to get underway at the High Court in Belfast on Monday. But, following out of court discussions, a judge was informed that the case was no longer proceeding.
Senior counsel for Duffy asked Mr Justice Gillen: "Would your lordship by consent enter judgment for the defendants against the plaintiff, with no order for costs."
Duffy had issued proceedings over his detention following the IRA murders of Constables David Johnston and John Graham.
The pair were gunned down while on foot patrol in Lurgan in June 1997.
Duffy was initially accused of the murders but, months later, the charges were dropped due to insufficient evidence. He has always denied any involvement in the killings.
His civil action was listed for a five-day hearing before lawyers confirmed that it would not be proceeding. Duffy is not liable for costs because he had secured legal aid.