Tanguay began his education in Quebec, graduating with a lauréat diploma from the Académie de musique du Québec (AMQ); Georges-Émile then moved to Montreal and took lessons with Arthur Letondal. Between 1912 and 1914, Tanguay lived in France, studying organ with Louis Vierne and harmony with Félix Fourdrain in Paris. Georges-Émile traveled across the Atlantic and lived in New York City for several years, further trained on organ by Pietro Alessandro Yon and Gaston Dethier. In 1920, Tanguay returned to Paris and studied with Vincent d'Indy at his [url=https://discogs.com/label/712984]Schola Cantorum[/url]; in the next five years, he took more organ and piano lessons with Édouard Mignan and [url=https://discogs.com/artist/3244818]Simone Plé-Caussade[/url].

In 1925, Georges-Émile Tanguay came back to Canada, taking the organist post at Montréal's Église de l'Immaculée-Conception church. He began teaching in the 1930s and held several faculty positions at Conservatoire National de musique in Montreal, a joint Conservatoire de musique du Québec à Montréal (CMQM) when it launched in 1943, and later taught at Canadian Music Centre and privately. Some of Tanguay's notable students include Léon Bernier, Maurice Blackburn, Marcel Laurencelle, André Mérineau, Renée Morisset, and Micheline Tessier.