In 2005 he was unanimously elected President and Treasurer of the Board of Directors of the Onassis Foundation.
In 2006, A. Papadimitriou was awarded the St. Mark’s Cross by the Patriarchate of Alexandria. In 2008, A. Papadimitriou was accepted as Honorary Master of the Bench of the Middle Temple. In 2010 he was decorated with the insignia of the Knight of the Legion of Honor (Chevalier de la Légion d' Honneur) by the Government of France. In 2012 he was awarded the degree of Doctor of Philosophy, Honoris Causa, by the University of Haifa. In 2014 he was awarded the Grand Commander of the Order of the Phoenix by the President of the Hellenic Republic. In 2015 he was named a Doctor of Science of City University London.