The State will not appeal a High Court judgment made earlier this month that rejected the extradition of Ian Bailey to France.
Mr Justice Paul Burns also awarded costs against the State at the High Court hearing.
An approved copy of the judgment made on 12 October will also be made available to French authorities.
Mr Bailey did not make an appearance at the High Court and has denied any involvement in the death of Sophie Toscan du Plantier in west Cork in 1996.
French authorities were seeking Mr Bailey's extradition to serve a 25-year prison sentence imposed on him by a French court.