Kouvelas was born in Amaliada, Elis prefecture in the Peloponnese on May 26, 1936. He holds degrees in Civil Engineering from the Polytechnic School of Thessaloniki, as well as Law from the University of Thessaloniki. He did graduate studies in France.
He has served in several New Democracy cabinets as:
- Minister for the Environment, Physical Planning and Public Works (1989)
- Minister for Culture (1989)
- Minister for the Interior (April 1990- August 1991)
- Minister for Agriculture (August 1991- October 1991)
Kouvelas is married to the former Niki Alexaki. The couple have two sons and one daughter. He speaks French and English.