Born at Ruvo di Puglia (Province of Bari, Apulia) into a family of humble means, Cotugno underwent physical and economic hardships to get an education.

He was sent to nearby Molfetta for training in Latin, returning to Ruvo for work in logic, metaphysics, mathematics, physics, and the natural sciences.

In 1765 he made trips to Rome and northern Italy to visit libraries and men of science, including Giovanni Battista Morgagni (1682–1771), and in 1789 he travelled to Austria and Germany as physician to Ferdinand IV, king of Naples.

An outstanding example of the physician–humanist, Cotugno was devoted to books and accumulated a large library, was well versed in art, architecture, numismatics, and antiquities, and had a great facility in the Latin language.

In the same year his anatomical dissertation De aquaeductibus auris humane internae, following the work of Guichard Joseph Duverney and Antonio Maria Valsalva and anticipating that of Hermann von Helmholtz, described the vestibule, semicircular canals, and cochlea of the osseus labyrinth of the internal ear, demonstrated the existence of the labyrinthine fluid, and formulated a theory of resonance and hearing.