Twenty-three children aged between nine and 16 who were shown being abused have been identified.
According to the European police force, Europol, the network created videos tailor-made to order of children being abused and sold them to 2,500 customers in 19 countries.
The arrests included not only the network's operators but also its clients who viewed the explicit images.
Europol analyst Menno Hagemeijer said they had tracked down large numbers of people who had paid to see the videos and photos.
He said pictures were found of children being forced to hold a piece of paper with the name of a ring member.
In the Republic of Ireland, five searches were carried out during the summer and a number of seized computers are undergoing forensic examination.
The investigation began in July 2006, when police in Australia found a video on the internet showing an adult abusing two young girls.
The girls were identified by police in Belgium and the offender, their father, was arrested.
He in turn led investigators to the producer of the video, an Italian man who operated in Belgium and the Netherlands but also owned a studio in Ukraine.