European police agency Europol said visas and passports were sold for up to £2,500 ($3,600) and sent across the EU, Africa, the Middle East and Asia.
Greek police said the criminal networks were also involved in smuggling people across borders.
About 100 people are still wanted in Greece and other countries.
Europol said the network was based in Athens and consisted of two criminal groups, one run by Sudanese people and another by Bangladeshis, and 16 people have been arrested in Greece.
Both groups forged passports, national ID cards, Schengen visas, driving licences, asylum seekers' registration cards and residence permits, police said.
Ten suspects were arrested in the Czech Republic, where a separate group would send stolen or lost travel documents to Athens for the Bangladeshi and Sudanese groups to falsify.
A police spokesman in the Czech Republic said seven migrants were also arrested for using forged documents.
The Sudanese-led group helped up to 15 migrants a month enter the EU at a cost of up to nearly £4,000 ($5,800, €5,200) per head, Greek police said. Read more here at BBC