Elline Marie Asisoff was born Elline 'Line' Eyermann in Copenhagen, Denmark on August 19, 1895 to Ane Cecile and Frederick P. Eyermann, a parish priest. The eldest of three girls, they would frequently spend time outdoors in the landscapes of Falster and Fjerritslev where they were raised, a pastime she later credited with inspiring her artistic pursuits. In 1909 their father passed away unexpectedly, and the girls were sent to live with their relatives in Charlottelund. Asisof had intended to become a teacher and studied at the Pan Ordrup Gymnasium, but was soon encouraged by her professor, Georg Christensen, to consider becoming an artist instead due to her talent in painting and drawing. After graduation, she enrolled at the Charlottenborg Art Academy.

Around 1919 she began to establish an artistic reputation with the entrance of her work in the Charlottenborg annual exhibition. Receiving critical praise, her work was then published in The Studio magazine. Before long she found regular work as a painter, illustrator, poster designer, and author (under the name "E.E. Asisoff").

In 1922 she married fellow Academy painter Kasro Asisoff (1884-1958) and together they had one child, Per Asisoff (1923-1981). She continued to work as an artist until late in life.

Elline Eyermann Asisoff died on January 1, 1982 in Lyngby, Denmark.