He has held many visiting appointments in the United States, Europe and Asia, including the University of California, Berkeley, Stanford University, Yale University, Swiss Federal Institute of Technology and Tokyo Institute of Technology.

Professor Anderson has served as a member of a number of government bodies, including the Australian Science and Technology Council and the Prime Minister's Science, Engineering and Innovation Council. He was a member of the Board of Cochlear Limited, the world's major supplier of cochlear implants, from 1995 to 2005. He is a Fellow of the Australian Academy of Science and Academy of Technological Sciences and Engineering, the Institute of Electrical and Electronic Engineers, and an Honorary Fellow of the Institution of Engineers, Australia. In 1989, he became a Fellow of the Royal Society, London, and in 2002 a Foreign Associate of the US National Academy of Engineering. He holds honorary doctorates of the Catholic University of Louvain in Belgium, the Swiss Federal Institute of Technology, and the Universities of Sydney, Melbourne, New South Wales and Newcastle. He was appointed an Officer of the Order of Australia in 1993 and received the Japanese Order of the Rising Sun with Neck Ribbon and Gold Rays in 2007.

He was President of the International Federation of Automatic Control for the triennium 1990 to 1993, and served as President of the Australian Academy of Science for four years from 1998 to 2002.