During the five decades of his poetic career, Ammons was the recipient of many awards and citations. Among his major honors are the 1973 and 1993 U.S. National Book Awards (for Collected Poems, 1951-1971 and for Garbage); the Wallace Stevens Award from the Academy of American Poets (1998); and a MacArthur Fellowship in 1981, the year the award was established. A school in Miami, Florida was named after him.
Ammons's other awards include a 1981 National Book Critics Circle Award for A Coast of Trees; a 1993 Library of Congress Rebekah Johnson Bobbitt National Prize for Poetry for Garbage; the 1971 Bollingen Prize for Sphere; the Poetry Society of America's Robert Frost Medal; the Ruth Lilly Prize; and fellowships from the Guggenheim Foundation and the American Academy of Arts and Letters. He was elected a Fellow of the American Academy of Arts and Sciences in 1978.