George Elbert Burr’s earliest instruction in drawing and painting was provided by his mother and he made his first attempts at etching in the early 1870s. In December 1878, Burr enrolled in the Chicago Academy of Design (now the School of the Art Institute of Chicago) but he terminated his studies in April of the following year. In 1888 he was creating illustrations for Schribner’s and Harper’s magazines as well as for John Muir’s Picturesque California, and, after moving to New York, he illustrated for Cosmopolitan and Leslie’s.

In 1906, Burr and his wife, Elizabeth, moved to Denver. A few of his color etchings were included in the 1915 Panama Pacific International Exposition and the following year he was represented by two etchings in the First Annual Exhibition of the Brooklyn Society of Etchers at the Brooklyn Museum. In 1921 he copyrighted the last of the thirty-five etchings in the Desert Set, which was circulated in exhibitions by the American Federation of Arts. For health reasons, Burr had to leave the winter chill of Denver and purchased a home in Phoenix, Arizona in 1927.

Burr was a member of the American Institute of Graphic Arts; Arizona Society of Artists; Brooklyn Society of Etchers; Cactus Club, Denver; California Society of Etchers; Denver Art Association; National Arts Club of New York; New York Society of Etchers; Phoenix Fine Art Association; Print Makers’ Society of California; and Société aux Etats-Unis. He served as the first president of the Denver Art Association and president of the Phoenix Art Association. During his lifetime Burr's work was exhibited at the Bibliothèque Nationale, Paris; the British Museum, and the Victoria & Albert Museum, London; the National Museum and the Smithsonian Institution, Washington D.C.; and the Brooklyn Museum.