Morishita was born in Okayama Prefecture. He graduated from Osaka University Medical School in 1987 and finished his postdoctoral research at Stanford University School of Medicine in 1991. He was appointed as Associate Professor, Department of Geriatric Medicine, Osaka University Graduate School of Medicine in 2003.
Morishita is currently a member of the Intellectual Property Policy Committee, Structural Reform Council, Ministry of Economy, Trade and Industry. He is also a member of the Council for Science and Technology, Ministry of Education, Culture, Sports, Science and Technology. From 2003 to 2007, Morishita served as a member of the Intellectual Property Strategy Headquarters (Director General: Prime Minister).