Professor Webb began his appointment as the second Vice Chancellor of Griffith University in 1985. He had been hand picked by foundation Chancellor Sir Theodor Bray to succeed the University's pioneering foundation Vice Chancellor, Professor John Willett. Professor Webb had enjoyed a distinguished academic and professional career before his tenure began with Griffith University. He held high level positions at both University of Melbourne (Australia) and Cornell University (USA) in an academic capacity, acted as a United Nations economic advisor to the Malaysian Government, and served as the President of the Victorian Branch of the Economic Society of Australia.

Professor Webb worked diligently to expand the University into a multi-campus organisation and increase Griffith's profile at both national and international level. He oversaw four successful amalgamations with other learning institutions and the construction of Griffith University's Logan Campus. This expansion saw the organisation grow from one, to its current five campus operation. Professor Webb also improved the University's research and educational profile, establishing over 50 new research centres, institutes, and units.

Upon his retirement in 2002, Professor Webb had been the longest serving (17 years) Vice Chancellor of any Australian University. His contributions to the academic community have been widely acknowledged. Both the University of Melbourne and Griffith University have conferred the title of Professor Emeritus upon him. He has also received honorary Doctoral degrees from the Queensland University of Technology and the University of Southern Queensland. The Webb Centre at Griffith University's Queensland College of Art (Southbank) takes his name and Professor Webb was made an Officer of the Order of Australia on the Queen's Birthday 2003.