The courts contain state of the art facilities for victims and for child witnesses.
The juries will be completely secured and separated from the public during the course of trials.
The building will have 22 courtrooms, housing all criminal courts - the District Court, the Circuit Criminal Court, the Central Criminal Court, the Special Criminal Court and the Court of Criminal Appeal.
The Courts Service says the facilities for victims of crime in the new building are the best in the world.
A special children's evidence suite has also been designed following consultation with Barnardos.
The building will begin full sittings in January.
The juries will no longer be minded by gardaí but by civilian jury minders.
Mr Justice Paul Carney will hold the first sittings of the Central Criminal Court in the new building on Wednesday.
The District Court will begin hearings next month and all the criminal courts will be operating in the new building from 11 January.
