Fulton was born and raised in Troy, New York, the youngest of three daughters. Her father was the proprietor of the historic Phoenix Hotel, and her mother was a visiting nurse. She began writing poetry in high school. In 1979 she attended a women's poetry conference in Amherst, Mass., which she would later cite as a formative experience. While an undergraduate, she received competitive scholarships to study poetry with Thomas Lux at The Writers Community in New York City. In 1980 she married Hank De Leo and moved to Ithaca, New York, to study poetry under A.R. Ammons, Phyllis Janowitz, Kenneth McClane, and Robert Morgan in Cornell University's Creative Writing Program. While at Cornell, her first book was selected by W.D. Snodgrass for the Associated Writing Program's publication prize. After receiving her MFA, she was a fellow at The Fine Arts Work Center in Provincetown. In 1983 Fulton moved to Ann Arbor, Michigan, for a 3-year appointment as Fellow in the Michigan Society of Fellows. Mark Strand selected Fulton’s second book, Palladium, for publication in the 1985 National Poetry Series. In the interdisciplinary Society of Fellows she further developed her interest in using scientific metaphor and began her lifelong friendship with John H. Holland. She has often cited Holland's writing on Complex Adaptive Systems as being instrumental in the development of her theory on Fractal Poetics [see Fulton's prose collection]. It was also where she met the composers William Bolcom and Enid Sutherland. In 1991 Fulton was awarded a MacArthur "Genius Grant" Fellowship.
In addition to poetry, Fulton has written essays and criticism and has been widely praised for her finely crafted and emotionally powerful short fiction. The Nightingales of Troy collects the ten stories she had published before 2008. Two of those stories were selected for inclusion in The Best American Short Stories. Three contemporary authors share the distinction of appearing in both The Best American Short Stories and The Best American Poetry series: Alice Fulton, Lydia Davis, and Stuart Dybek.
Alice Fulton was a senior fellow in the Michigan Society of Fellows from 1996 to 2000. She remained at University of Michigan until 2002, when she returned to Ithaca as the Ann S. Bowers Distinguished Professor of English at Cornell University. In 2011 she received an American Academy of Arts and Letters Award in Literature. The Library of Congress awarded Fulton the Rebekah Johnson Bobbitt Award in 2002. In 2004 she was the Holloway Lecturer in the Practice of Poetry at University of California, Berkeley, and in 2010 she was the George Elliston Poet at University of Cincinnati. She has also been a visiting professor at University of California, Los Angeles, University of Virginia, Charlottesville, and a number of other universities.