The State will not appeal against the High Court's decision last month to refuse the extradition of Ian Bailey to France in relation to the death of Sophie Tuscan du Plantier.
Mr Bailey (aged 60) of The Prairie, Liscaha, Schull, west Cork, denies any involvement in the death of Ms du Plantier, who was found dead outside her holiday home in Schull in December 1996.
French authorities previously sought the surrender of Mr Bailey in 2010 but this application was refused by the Supreme Court in 2012. A second extradition request was transmitted to Ireland last summer, seeking the surrender of Mr Bailey for alleged voluntary homicide.
French authorities have previously prosecuted people for crimes committed against French citizens outside of France.
Mr Bailey, who claims gardaí tried to frame him for the killing of Ms du Plantier, could be tried in France in his absence.
Last month, Mr Justice Tony Hunt refused to order the extradition, dismissing the Minister for Justice's application as an "abuse of process", among other reasons.
During today's brief hearing, for which Mr Bailey was absent, solicitor Gareth Lynch told the court that the State was not going to appeal the matter.
Garrett Simons SC, for Mr Bailey, then appealed to the court for costs.
Mr Justice Hunt consented to the application, awarding the costs of the case to Mr Bailey, certifying for two senior counsel.