The European Commission has decided to invest €200 million (£125 million) more in a European equivalent of the Fulbright programme.
Erasmus World will open universities in the European Union to scholars and postgraduate students from other countries.
The scheme, launched in Brussels by education commissioner Viviane Reding, will provide 250 European masters courses and some 4,200 scholarships worth about £1,000 a month to students. It will run from 2004 to 2008.
Ms Reding said that EU universities took too few students and visiting scholars from other continents and that this affected the EU's "cultural, political and economic influence in the world".
The initiative does more than rehash existing programmes. Region-based projects such as Tempus (serving the former USSR, western Balkans and Mediterranean Basin) and agreements with the US, Canada, Latin America, Asia and Australia will stay in place, as will projects for bringing in students from EU-entry candidate countries.
Commission education spokesman Christophe Forax said: "Erasmus World is entirely new and does not take the place of any existing scheme."
Universities in eastern European countries applying to join the EU will be eligible for Erasmus World, but the commission declined to say whether existing schemes for such students would continue to be funded when their term expired. This would normally be after five years, by which time many of the countries will be full EU members.
Erasmus World will provide scholarships for European students and scholars to go to third-world countries. Between now and 2008, almost 4,000 European postgraduate students and 800 European visiting scholars could receive support from the scheme.
About 122,000 of the 400,000 foreign students in the EU attend UK universities, and prime minister Tony Blair wants to increase the number of foreign students in the UK by 50,000 by 2005.
The commission is not entirely happy about the concentration of international students in Britain, and it has made it a condition of the Erasmus masters courses that study involve at least three universities from three EU states.