He was born in Vigevano, Italy, where he lived until he was 13 years old. At that time his family fled Italy because his father, Giovanni Rota, was likely to be an object of fascist persecution.

He attended the Colegio Americano de Quito in Ecuador, and earned degrees at Princeton University and Yale University. For most of his career he was a professor at the Massachusetts Institute of Technology, where he was the only person ever to be appointed Professor of Applied Mathematics and Philosophy. He was also the Norbert Wiener Professor of Applied Mathematics.

Rota was one of the most respected and popular teachers at MIT. He taught a difficult but very popular course in probability, which MIT has not offered again. He also taught Applications of Calculus, and Differential Equations. His philosophy course in Phenomenology was offered on Friday nights to keep the enrollment manageable. Among his many eccentricities, he would not teach without a can of Coca-Cola, and handed out prizes ranging from Hershey bars to pocket knives to students who asked questions in class or did well on tests.

From 1966 until his death he was a consultant at Los Alamos National Laboratory, frequently visiting to lecture, discuss, and collaborate, notably with his friend Stan Ulam.

He began his career as a functional analyst, but changed directions and became a distinguished combinatorialist. His series of ten papers on "Foundations of Combinatorics" in the 1960s is credited with making it a respectable branch of modern mathematics. He said that the one combinatorial idea he would like to be remembered for is the correspondence between combinatorial problems and problems of the location of the zeroes of polynomials. He worked on the theory of incidence algebras (which generalize the 19th-century theory of Möbius inversion) and popularized their study among combinatorialists, set the  umbral calculus on a rigorous foundation, unified the theory of Sheffer sequences and polynomial sequences of binomial type, and worked on fundamental problems in probability theory. His philosophical work was largely in the phenomenology of Edmund Husserl.

He died suddenly in Cambridge, Massachusetts while reading at home. A reading room in the Department of Mathematics at the Massachusetts Institute of Technology is dedicated in his name.