Alonso was born in Havana, and attended Spring Hill College in Mobile, Alabama.
On returning to Cuba, he began ballet training in 1932 at the Sociedad Pro-Arte Musical arts school in Havana with Nikolai Yavorsky.
He subsequently danced with the Ballet Theatre from 1943 to 1945, in works created by Fokine, George Balanchine and Leonid Massine.
Later he married Elena del Cueto, a Cuban dancer, until 1962, when she left for the United States with their two daughters.
Alonso died from heart failure in his adopted hometown of Gainesville, Florida, at age 90.