At three years of age young Edmund was brought to America from his homeland of Armenia. His formal education started at the Rhode Island School of Design, but in 1930 he moved to NYC and studied at the Art Students league under van Schlegal and Stuart Davis. He later went on to become an instructor at the school. His early work shows the influence of the Ashcan School. In 1945 after serving for a year at the University of Missouri, Yaghjian took the post of chairman of the Department of Fine Arts at the University of South Carolina. A position he held for 21 years.
Yaghjian has had one man exhibitions at the Kraushaar Galleries, New York City; Mint Museum, Charlotte, N.C.; Gibbes Museum, Charleston, S.C. among others. He has exhibited work at the Metropolitan Museum, Whitney Museum, Corcoran Museum, St. Louis Museum, Pennsylvania Academy, and the Butler Museum of Art, for example.