Couper was the only surviving son of a wealthy textile mill owner near Glasgow.

He began the formal study of chemistry at the University of Berlin in the autumn of 1854, then in 1856 entered Charles Adolphe Wurtz's private laboratory at the Faculty of Medicine in Paris (now the University of Paris V: René Descartes).

Couper's idea that carbon atoms can link to each other following valence regularities was independent of a paper by August Kekulé proposing the same concept.

But his health was now broken, and he did no more serious work, spending the last 30 years of his life in the care of his mother.

In this respect, his work was probably influential on the early structural theorists Aleksandr Butlerov and Alexander Crum Brown.