According to this page it is sponsored by the Stiftung Atlantik-Brücke, Daimler Chrysler AG, Boeing International, the German Marshall Fund, the Bundesverband der Volks- und Raifeissenbanken and the Bankhaus Löbbecke. In addition, the founders have put in some of their own capital.

It doesn't produce annual reports on its website. In general I find that American charities are much more transparent in that regard than European charities. That's probably a requirement by law, and the EU should address that issue.

Full disclosure: I write a blog with Joerg who works at the Atlantische Initiative and on the Atlantic Community. The blog is otherwise not affiliated with the Atlantische Initiative.