Alexander Dzigurski was born in Yugoslavia as the son of a wheat farmer. Dzigurski began his studies at the School of Art, Belgrade and the Academy of Art in Munich, Germany. As a young artist he was commissioned to paint the interiors of churches, an interest he would continue to pursue throughout his career. During the 1930s Dzigurski volunteered in the navy for the Kingdom of Yugoslavia, which began his fascination with painting the sea.

With the onset of WWII, Dzigurski and his family immigrated to the United States. After working on the East Coast for a short time, Dzigurski settled his family in California and continued to pursue his career as an artist. He began painting the rocky coastlines of California and Oregon. Dzigurski traveled widely throughout the United States, where he painted the Rocky Mountains, Grand Tetons, Glacier National Park, and New England.

He was a member of various organizations including the Fine Art Institute of Los Angeles; American Artists Professional League; and Society of Western Artists. His work has been exhibited in the following museums: Belgrade Art Museum, Yugoslavia; Ford Museum, Detroit; and Boston Museum of Fine Arts.