Born in Brussels, a scion of the Borchgrave-d’Altena family, Elie Borgrave was destined to a career in the diplomatic service. However, his predilection for meditation turned his attention to the arts. Elie obtained a BA in Literature and Philosophy and decided to be a painter following a trip to Paris during 1937-38. In 1940, Borgrave a meeting with Jankel Adler in London informed his early figurative expressionist style. As of 1955-56, Borgrave turned to Abstraction. During the 1950s and 1960s Borgrave and his young family lived between Belgium, France, Italy and the USA.

His works were exhibited at the Galerie Louis Manteau (Brussels), the New Art Circle of Isreal Ben Neumann (New York), the Stable Gallery of Eleanor Ward (New York), who also organised early shows of Robert Indiana and Andy Warhol. During the 1960s and 1970s, Borgrave's work was exhibited by Galerie Veranneman (Brussels) and Museum d’Hondt-Dhaenens (Ghent). In 1963, Borgrave had a first museum exhibition at the Palais des Beaux Arts, Brussels.
In 2017 a large retrospective was held at the Museum of Ixelles, where his work was rediscovered by the general public.