After graduating from the University of Bucharest with a degree in natural sciences, he became a teacher at Craiova in 1887.
He then transferred to Traian High School in Turnu Severin, building up the new institution.
He was responsible for several new school buildings in the local Mehedinți County.
Costescu served the county as prefect, senator and, from 1912, Conservative-Democratic deputy.
He served as a general secretary in the Ministry of Industry.