Bossuyt obtained a Dr.iur (LLM) at the University of Ghent in 1968, a Certificate of international relations at Johns Hopkins University in Bologna in 1969, and a Ph.D. in political science from the Graduate Institute of International Studies in 1975. He is professor emeritus of international law at the University of Antwerp.
He was appointed to the Constitutional Court by Royal Order on 28 January 1997. From 9 October 2007 until his retirement Bossuyt was the President of the Dutch linguistic group of the Constitutional Court of Belgium. He was ennobled as a baron in the 2009 honours list. Upon reaching the mandatory retirement age of 70 years, Bossuyt retired from the Court and became President-Emeritus.
Bossuyt was a member of the UN Committee on the Elimination of Racial Discrimination (2000-2003, 2014-present).