Cannon started her academic career in 1974 at Stockholm University, where she held various positions, including a research associate at the Wenner-Grenn Institute from 1974 to 1980. Subsequently, she served as an associate professor from 1980 to 1983 and then as a professor of physiology from 1983 to 2013. Since 2013, she has held the title of emeritus professor at Stockholm University.
Cannon's involvement with the Royal Swedish Academy of Sciences included a tenure as vice president from 2003 to 2008 and subsequently as president from 2012 to 2015. Furthermore, she played an important role in the Nobel Foundation, serving as a member of the Trustees from 2006 to 2011 and taking on the role of chairman from 2008 to 2011.