Daughter of a Methodist minister, Eliza Pratt was born in Manorhamilton, Ireland. She moved with her family to New York in 1840 and in 1849 married Henry Wellington Greatorex, a musician. Between 1854 and 1856, Greatorex studied with William Wotherspoon and the Hart brothers in New York; at that time, she exhibited some preliminary drawings, but it was not until she was widowed in 1858 that she began the full-time pursuit of art, supporting herself and her children with her work and by teaching at a girls’ school for fifteen years.

She studied painting with Emile Lambinet in Paris in 1861/62, and in 1870, mother and daughters studied at the Pinakothek in Munich. In 1879, Greatorex went to Paris, where she trained in engraving with Charles Henri Toussaint in order to maintain greater control over the quality of reproductions of her work. There she and her daughters remained. Greatorex is most strongly identified with the Hudson River School, and her work is broadly held by institutions in both the United States and Europe. She died and is buried in Paris.