Meléndez taught at the University's high school while she continued to pursue her University studies. In 1924, she received her Bachelor's degree and soon after went to New York where she obtained her Master's Degree in 1926 from Columbia University. She returned to Puerto Rico where she became a professor at the University of Puerto Rico.
Meléndez later went to Mexico where she enrolled in the National University of Mexico (UNAM). In 1932, she became the first woman in the history of Mexico to earn a Doctorate in philosophy and letters.
When she returned to Puerto Rico, the University of Puerto Rico bestowed upon her the title of "Professor Emeritus" in Hispanic-American Literature. She was named director of the Hispanic Studies and Humanities Faculty Department at the University, a position she held between 1940-1959. Concha also founded the Tenure on Hispanic-American Literature in the University. In 1964, Concha acted as visiting professor at the Middlebury School of Languages in Vermont. Concha Melendez died in San Juan, Puerto Rico on June 26, 1983.
Melendez's works have been compiled into 15 volumes by the Editorial Cultural. Amongst these are:
Melendez was awarded many honors and distinctions in Puerto Rico and other countries. Amongst the awards are:
A center of the Biblioteca Nacional de Puerto Rico del Instituto de Cultura Puertorriqueña is named after her. Every year the Coalition of Hispanic American Women of Miami, selects five high school graduates, whom will receive the Elena Mederos/Concha Melendez Scholarship for their outstanding academic records. Puerto Rico has a school in San Juan named after her and in Virginia there is also a high school named after her.