He was born in Sotaquí, Coquimbo, on 8 May 1920, the son of Félix Iglesias and Laura Cortés. He married María Pinto Argandoña and they had seven children.
He studied at the Conciliar Seminary of La Serena and later entered the Faculty of Chemistry and Pharmacy at the University of Chile, graduating as a chemist-pharmacist in 1942. From 1945 to 1955, he owned the "Iglesias" pharmacy in Ovalle, and from 1956 to 1965, he owned the "Esmeralda" pharmacy in Los Andes. Between 1950 and 1953, he was a counselor of the Regional College of Chemists-Pharmacists of Atacama and Coquimbo. He was also a member of the Colegio de Químico-Farmacéuticos de Chile and of the Union of Pharmacy Owners.
During his university years, he was a student leader at the Faculty of Chemistry and Pharmacy and a delegate of the same faculty to the Federation of Students of the University of Chile (FECH).
He joined the Falange Nacional in 1946, and in 1957 he became a member of the Christian Democratic Party (PDC). Between 1960 and 1961 he served as provincial president in Aconcagua and as a delegate to several congresses.
He was municipal councilman and mayor of Ovalle from 1953 to 1956.
In the 1965 elections, he was elected Deputy for the 5th Departmental Group "San Felipe, Petorca and Los Andes" for the legislative period 1965–1969. He joined the Permanent Commission on Medical-Social Assistance and Hygiene, and the Special Commission on Private Requests (1967).
In the 1969 elections, he was re-elected Deputy for the same constituency, for the 1969–1973 legislative period. He was part of the Permanent Commission on Finance, the Special Commission on Labor Situation at the Andina Mine (1969–1970), the Special Commission on the Constitutional Accusation against the Minister of Economy Pedro Vuskovic, and the Joint Budget Commission.
He was not re-elected in the 1973 elections.
Félix Iglesias Cortés died on 8 October 2005.