Kelly studied art in Paris from 1948 to 1954, when post-war Paris was the home of European Abstraction and the avant-garde*. He enrolled at the Ecole des Beaux-Arts* in Paris under the G.I. Bill, although he attended classes infrequently. In France, he discovered Romanesque* art and architecture and Byzantine art. He was also introduced to Surrealism* and Neo-Plasticism*, which led him to experiment with automatic drawing and geometric abstraction*.

In 1950, Kelly met Jean Arp and that same year began to make shaped-wood reliefs and collages* in which elements were arranged according to the laws of chance. He soon began to make paintings in separate panels that can be recombined to produce alternate compositions, as well as multi-panel paintings in which each canvas is painted a single color. During the 1950s, he traveled throughout France, where he socialized with Constantin Brancusi, Alexander Calder, Alberto Magnelli, Francis Picabia, Georges Braque, Alberto Giacometti, Joan Miro and Georges Vantongerloo , among other artists. His first solo show took place at the Galerie Arnaud, Paris, in 1951.

After six formative years in Paris, Kelly returned to the United States in 1954, living first in a studio apartment on Broad Street, and then at Coenties Slip in lower Manhattan, where his neighbors included Robert Indiana, Agnes Martin, Fred Mitchell, James Rosenquist, Lenore Tawney, and Jack Youngerman. At this time he "used his canvases to explore the concept of spectral color and expressed his fascination with the resonance of color."

His first solo show in New York was held at the Betty Parsons Gallery in 1956, and three years later he was included in Sixteen Americans at the Museum of Modern Art, New York. In 1958, he also began to make freestanding sculptures. He moved out of Manhattan in 1970, set up a studio in Chatham, and a home in nearby Spencertown, New York.

Kelly's first retrospective was held at the Museum of Modern Art, New York, in 1973. The following year, Kelly began an ongoing series of totemic sculptures in steel and aluminum. He traveled throughout Spain, Italy, and France in 1977, when his work was included in Documenta in Kassel.

He has executed many public commissions, including a mural for UNESCO in Paris in 1969, sculpture for the city of Barcelona in 1978, and a memorial for the United States Holocaust Memorial Museum, Washington, D.C., in 1993.

Kelly's extensive work has been recognized in numerous retrospective exhibitions, including a sculpture exhibition at the Whitney Museum of American Art, New York, in 1982; an exhibition of works on paper and a show of his print works that traveled extensively in the United States and Canada from 198788; and a career retrospective in 1996 organized by the Solomon R. Guggenheim Museum, New York, which traveled to the Museum of Contemporary Art, Los Angeles; the Tate Gallery, London; and the Haus der Kunst, Munich. Kelly lives in Spencertown, New York.