Eamonn Harrison, from Northern Ireland, is wanted in connection with the discovery of the bodies in a refrigerated container.
Mr Justice Donald Binchy said that after receiving comprehensive arguments from both sides, he decided to approve the extradition.
Justice Binchy said he has not published his judgment in full to the court and will not make it available until Monday.
He said it would not be helpful for him to try and summarise his decision to the court.
Defence counsel Tony McGillicuddy said he will read the judgment next week and decide whether to lodge an appeal.