He graduated from the University of Havana School of Law. Dr. Agramonte was also the Dean of School of Philosophy and Letters at the University of Havana. From 1947 to 1948, he was the Ambassador of Cuba to Mexico. In 1948, he returned to Cuba to run for Vice-President of Cuba with Dr. Eduardo Chibás (as President).
He was the first Foreign Minister of the Cuban Revolution. He later resigned because of the Communist tilt of the government. In May 1960, he left Cuba for Puerto Rico with his family.