Costantino Nivola was born in Sardinia. He learned the trade of a stonecutter from his father, then studied art in Milan. In 1939 he left fascist Italy with his Jewish wife, Ruth Guggenheim, for the United States. He worked initially as a designer and became art director of Interiors magazine. Heavily involved in the post-war New York art scene, he eventually devoted himself full-time to art as his sand-cast relief sculptures gained fame. A 75-foot-long wall relief was made for the Olivetti showroom on Fifth Avenue, which opened to great acclaim in 1954, the same year Nivola became a professor and the director of the "Design Workshop" at Harvard. In 1962, after contributing a relief wall to the new International Legal Studies building at Harvard Law School, he returned to New York as Professor of Art at Columbia. When the Olivetti showroom closed in 1970, the panels went to the Science Center at Harvard and have been on view since 1973. Restoration of the relief's colors took place in 2005. In 2006, the Law School covered its Nivola relief with a plain wall adorned with modern art.

In mid-career, Nivola withdrew from the public arena and exhibitions and devoted himself to a vast, much more intimate body of terra-cotta, bronze, and marble sculptures. He gradually returned to large-scale stone, wood, and metal sculpture in the last few decades of his life. Nivola's grandson, Alessandro, born in Boston, has become a well-known actor.