He contributed to the fields of probability and statistics, and to their application to finance, demography and social sciences.

In particular, he formulated the Bienaymé–Chebyshev inequality concerning the law of large numbers and the Bienaymé formula for the variance of a sum of uncorrelated random variables.

Irénée-Jules Bienaymé continues the line of great French probability thinkers that began with Blaise Pascal and Pierre de Fermat, then carried on with Pierre-Simon Laplace and Siméon Denis Poisson.

He translated into French the works of his friend the Russian mathematician Pafnuty Chebyshev, and published the Bienaymé–Chebyshev inequality which gives a simple demonstration of the law of large numbers.

Bienaymé criticized Poisson's "law of large numbers" and was involved in a controversy with Augustin Louis Cauchy.

It is now known that ordinary least squares is the best linear unbiased estimator, provided errors are uncorrelated and homoscedastic.