In 1951, after only a few years in Australia, he returned to the UK to accept the Beyer Chair in Engineering at the University of Manchester.
When Monash opened, Matheson led and oversaw rapid development, from an empty site in Clayton, to a university recognised internationally for excellence in research and teaching.
In an article written shortly after his death, the Australian Academy of Technological Sciences and Engineering observed that "it is hard to imagine how Matheson could have built the university better.
During his term as Vice-Chancellor, he sat on the Royal Commission on the collapse of Melbourne's King Street Bridge (from 1962 to 1963).
He received Honorary Doctorates from Hong Kong, Manchester, Melbourne and Monash Universities.