He was Maître de Conférences at Lille University of Science and Technology in 1892-1893, then moved at Toulouse and Lyon.

He presided over entrance examinations at the École Polytechnique.

As director of École Normale Supérieure until 1935, he overviewed the construction of its new physics, chemistry and geology buildings of 24, Rue Lhomond.

He was elected a member of the Académie des Sciences in 1943.

Vessiot's work on Picard–Vessiot theory dealt with the integrability of ordinary differential equations.