With a chemistry major, Norman Thomas Mortimer Wilsmore completed a Bachelor of Science at the University of Melbourne in 1890. He remained at the University to pursue chemical research and graduated two years later with a Masters Degree. In 1894 Wilsmore moved to the UK to study with Professor Sir William Ramsay and Norman Collie at University College. After three years there he moved to Germany's University of Göttingen to study physical chemistry. He spent four years working in Germany where he also studied physics and electrical engineering. Many valuable and influential research articles arose from his work in England and Germany.

Norman Wilsmore's next move was to Switzerland to advance his knowledge of technical chemistry. He soon became first assistant to Professor Richard Lorenz in the Department of Physical and Electro-chemistry at the Federal Polytechnic. In 1903 Wilsmore returned to organic chemistry and to University College, London. He made his way from Assistant to Assistant Professor before leaving for Australia in 1912/1913. He was offered the Chair of Physical Chemistry at Liverpool University, but declined having already accepted the post of Chair of Chemistry at the newly formed University of Western Australia.

The first 22 years of his tenure at the University were hard going and he had little time for research: there was little infrastructure, many regulations and course outlines to be drafted and much financial hardship caused by the War (1914-1918) and the Depression (1931). The War also saw Wilsmore return to London to work with the Department of Explosives Supply (January 1917 to April 1919). It wasn't until 1935 that the first permanent chemistry buildings were functional. Norman Wilsmore was forced to retire as Chair in 1937 due to the University's age-limit policy, but privately continued his research. He was such a respected teacher and mentor that chemistry graduates raised money to fund what is now known as the annual Wilsmore Prize for the most meritorious chemistry graduate at the University.

An active member of the Western Australia State Committee of the Australian Chemical Institute, Wilsmore was twice elected President. He was also General President of the Chemistry Council and original Fellow and Vice President of the Australian National Research Council.