Glenn was born in Toronto, Ontario, Canada, in 1940. He studied law at Queen's University and Harvard Law School and earned his doctorate in law at Strasbourg.
He started his career at McGill University in 1971, recruited by the Faculty of Law to help support the National Program. He became known as a respected scholar in the field of comparative law, specifically comparative civil procedure and private international law. He began publishing in the 1980s and continued for the majority of his career. He started as an Assistant Professor in 1971, rising to the rank of Associate Professor in 1973 and then to Full Professor in 1978, a rank that he held until his passing in 2014.
While he remained at McGill for his entire career, he also had the honor of serving as a visiting professor at a number of illustrious universities throughout the world, including the Université de Montréal (1973), the Université de Fribourg (1985), and the Université française du Pacifique (1992). He was also the Director of Studies at the Hague starting in 1977. In 2012, he was elected president of the American Society of Comparative Law.
In 2006, The Government of Québec recognized H. Patrick Glenn with the Prix Léon-Gérin in the science category.
He was married to Jane Matthews Glenn, another McGill University professor.
Glenn died on 1 October 2014. No information is presently available about the cause or manner of death.