De Cordoba was born in New York City to parents who were French and Cuban in origin.

In the sound era, his deeply resonant speaking voice made him perfectly suited to talking pictures and was active as a character actor in Hollywood, from the mid-1930s through to the end of his life.

He was most often cast as aristocratic, or clerical characters of Hispanic origin, as in The Keys of the Kingdom (1944), because of his last name as well as his royal bearing.

His "living skeleton" sideshow character hides fugitive Robert Cummings (and Priscilla Lane) in his carnival wagon overnight in the Alfred Hitchcock film Saboteur (1942).

The last film in which he appeared, a political drama set in an unnamed South American dictatorship, Crisis (1950), was released shortly after his death.