Kelly was born in Brooklyn, New York, to Samuel Jason and Margaret Rose Kelly née Kane, in 1935. He did his undergraduate studies at the City College of the City University of New York, graduating in 1955. He then spent three years at Columbia University.

Kelly has worked as a translator and teacher, most notably at Bard College, where he has worked since 1961. Kelly's other teaching positions have included Wagner College (1960—61), the University at Buffalo (1964), and the Tufts University Visiting Professor of Modern Poetry (1966—67). In addition, he has served as Poet in Residence at the California Institute of Technology (1971—72), Yale University (Calhoun College), University of Kansas, Dickinson College, and the University of Southern California.

Kelly has published more than fifty books of poetry and prose, including Red Actions: Selected Poems 1960-1993 (1995) and a collection of short fictions, A Transparent Tree (1985). Many were published by the Black Sparrow Press. He also edited the anthology A Controversy of Poets (1965). Kelly was of great help to the Hungryalist group of poets of India during the trial of Malay Roy Choudhury, with whom he had correspondence, now archived at Kolkata.

Kelly received the Los Angeles Times First Annual Book Award (1980) for Kill the Messenger Who Brings Bad News and the American Book Award, Before Columbus Foundation (1991) for In Time. He also serves on the contributing editorial board of the literary journal Conjunctions.

Books of poetry

• Armed Descent, New York: Hawk's Well Press, 1961.
• Her Body Against Time, Mexico City: Ediciones El Corno Emplumado, 1963.
• Round Dances, New York: Trobar Press, 1964.
• Enstasy, Annandale: Matter, 1964.
• Lunes/Sightings, with Jerome Rothenberg, New York: Hawk's Well Press, 1964.
• Words in Service, New Haven: Robert Lamberton, 1966.
• Weeks, Mexico City: Ediciones El Corno Emplumado, 1966.
• Song XXIV, Cambridge: Pym-Randall Press, 1966.
• Devotions, Annandale: Salitter, 1967.
• Twenty Poems, Annandale: Matter Books, 1967.
• Axon Dendron Tree, Annandale: Salitter, 1967.
• Crooked Bridge Love Society, Annandale: Salitter, 1967.
• A Joining: A Sequence for H:D:, Los Angeles:Black Sparrow Press, 1967.
• Alpha, Gambier, Ohio: The Pot Hanger Press, 1967.
• Finding the Measure, Los Angeles: Black Sparrow Press, 1968.
• Sonnets, Los Angeles: Black Sparrow Press, 1968.
• Songs I-XXX, Cambridge: Pym-Randall Press, 1968.
• The Common Shore, (Books 1 - 5) Los Angeles: Black Sparrow Press, 1969.
• A California Journal, London: Big Venus Books, 1969.
• Kali Yuga, London: Jonathan Cape, 1970. A Cape Goliard Book.
• Flesh Dream Book, Los Angeles: Black Sparrow Press, 1971.
• In Time, West Newbury: Frontier Press,1971
• Cities. West Newbury: Frontier Press, 1972.
• Ralegh, Los Angeles: Black Sparrow Press, 1972.
• The Pastorals, Los Angeles: Black Sparrow Press, 1972.
• Reading Her Notes, Uniondale: privately printed at the Salisbury Press, 1972.
• The Tears of Edmund Burke, Annandale, privately printed, 1973.
• The Mill of Particulars, Los Angeles: Black Sparrow Press, 1973.
• The Loom, Los Angeles: Black Sparrow Press, 1975.
• Sixteen Odes, Los Angeles: Black Sparrow Press, 1976.
• The Lady Of, Los Angeles: Black Sparrow Press, 1977.
• The Convections, Santa Barbara: Black Sparrow Press, 1977.
• The Book of Persephone, New Paltz: Treacle Press, 1978.
• Kill the Messenger, Santa Barbara: Black Sparrow Press, 1979.
• Sentence, Barrytown: Station Hill Press, 1980.
• Spiritual Exercises, Santa Barbara: Black Sparrow Press, 1981.
• The Alchemist to Mercury: an alternate opus, Uncollected Poems 1960-1980, edited by Jed Rasula, Berkeley: North Atlantic Books, 1981.
• Mulberry Women, with drypoints by Matt Phillips, Berkeley: Hiersoux, Powers, Thomas,1982.
• Under Words, Santa Barbara: Black Sparrow Press, 1983.
• Thor's Thrush, Oakland: The Coincidence Press, 1984.
• Not this Island Music, Santa Rosa: Black Sparrow Press, 1987.
• The Flowers of Unceasing Coincidence, Barrytown: Station Hill Press, 1988.
• Oahu, Rhinebeck: St Lazaire Press, 1988.
• Ariadne, Rhinebeck: St Lazaire Press, 1991.
• Manifesto for the Next New York School, Buffalo: Leave Press, 1991.
• A Strange Market, (Poems 1985-1988), Santa Rosa: Black Sparrow Press, 1992.
• Mont Blanc, a long poem inscribed within Shelleys, Ann Arbor, Otherwind Press, 1994.
• Red Actions: Selected Poems 1960-1993, Santa Rosa, Black Sparrow Press,1995.
• Runes, Ann Arbor, Otherwind Press, 1999
• The Garden of Distances, with Brigitte Mahlknecht, Vienna / Lana, Editions Procura, 1999
• Unquell the Dawn Now : a collaboration with Friedrich Holderlin Schuldt, McPherson, 1999
• Shame = Scham : a collaboration with Birgit Kempker, McPherson, 2005
• Samphire, Backwoods Broadsides Chaplet Series Nº 97 , 2006
• Threads, First Intensity Press, 2006
• May Day, Parsifal Editions, 2006

Plays

• Oedipus After Colonus, 2008

The play Oedipus After Colonus takes as its point of departure Oedipus at Colonus, by Sophocles. Robert Kelly's only play (2008), it was first performed in 2010 under the direction of Crichton Atkinson at the HERE Arts Center in New York City as a part of HEREstay Festival - September, 2010.

The fictional character Senator Robert Kelly, featured in the X-Men comic books and movies, is named after him. X-Men writer Chris Claremont chose the name in honour of his Bard College professor.