The case was heard at Dublin's Special Criminal Court
Liam Campbell, 39, from Upper Faughart near Dundalk in County Louth, was convicted of being a member of the unlawful organisation and sentenced at Dublin's Special Criminal Court.
Campbell had been linked by the BBC Panorama programme to the Omagh bomb of August 1998 when 29 people were killed, including a woman pregnant with twins.
Campbell was arrested on 3 October last year by Irish detectives as part of an ongoing investigation into dissident republican activities. Campbell had denied membership of either the Real IRA or Provisional IRA.
Sentencing the father of two, Mr Justice Barr said the Real IRA had been engaged in much criminal activity since 1997, when it broke away from the Provisional IRA.
"That conduct amounts to a grievous crime against the people of Ireland, north and south. Membership constitutes a serious criminal offence," he added.
After his arrest, Campbell declined to answer questions relating to his membership of an illegal organisation.
George Birmingham SC, prosecuting, said the court had been entitled under the Offences Against the State (Amendment) Act of 1998 to draw inferences from his silence.
Mr Justice Barr said: "The court infers from his silence on being asked about membership of the IRA that he was unwilling to admit that he was a member of that organisation.
Corroboration
"The court also regards his failure to answer such questions as amounting to corroboration of the opinion expressed by Chief Superintendent Finnegan that the accused was in fact a member of the IRA on October 3rd, 2000."
The case against Campbell consisted of the opinion of Garda Chief Superintendent Michael Finnegan, interviews carried out by police after his arrest and items that were found during a search of his home.
The court had previously ruled during the seven-day trial that the Real IRA was covered by the Unlawful Organisations Suppression Order of 1939, which outlawed the IRA.
Mr Justice Barr said: "The so-called Real IRA are on all fours with the original IRA as it existed in 1939 and have a similar philosophy, objectives and structure and members of the group are within the ambit of the Suppression Order of 1939."
Campbell was refused leave to appeal against his conviction and sentence.