He was born in 1899 in Kharkiv and studied at the studio of Princess Tenisheva in St. Petersburg. Later, he enrolled at Kyiv University, planning to study law, but the events of 1917 disrupted his plans. In 1918, Boris served in the army of Skoropadsky and intended to join the White Army, but he was captured, from which he escaped. In 1919, lacking funds, he emigrated to the USA. Upon arriving in New York, he began working in an engraving workshop. He started his career in America without knowing English: he cut labels in a printing house, worked as a bottle designer, and painted the walls of the restaurant The Russian Inn. His paintings were noticed by artist and art critic Guy de Bois. In 1926, he obtained U.S. citizenship, and in 1930, he married Elizabeth Snyder. He worked for magazines such as Time, Fortune, and Life, and in 1954, he published the book 'How I See,' for which he received prestigious awards as an illustrator.

Throughout his career, Artsybashev created illustrations for over 50 books, as well as numerous advertising materials and magazine covers.

He passed away on July 16, 1965, in Lyme, Connecticut.