In 1829 Verhulst translated John Herschel's Theory of light and published the paper. In 1835, Verhulst was appointed professor of mathematics at the University of Brussels where he offered courses on geometry, trigonometry, celestial mechanics, astronomy, differential and integral calculus, and the theory of probability. In 1841, Verhulst was elected to the Belgium Academy. By 1848, he became the Academy's president.

Verhulst's research on the law of population growth showed that forces, which tend to obstruct population growth, increase in proportion to the ratio of the excess population to the overall population. He proposed a population growth model which takes into account the possible limitation of population size due to limited resources. Verhulst's model is often called the "Logistic Growth Equation", or "Verhulst Equation". His model is considered an improvement over the Malthusian model, which assumes human population grows exponentially when plagues or other disasters do not occur.