Juliá was born and grew up in San Juan. He first came to attention while performing in a nightclub by actor Orson Bean who encouraged him to come to the United States. Juliá moved to New York City in 1964 and began studying drama with Wynn Handman. He soon found work in off-Broadway theater. In 1966, Juliá hooked up with theater impresario Joseph Papp and the New York Shakespeare Festival. His Shakespeareanan roles included Edmund in King Lear in 1973 and the title role of Othello in 1979. Juliá went on to enjoy great success on the musical stage, winning four Tony Awards for his roles in Two Gentlemen of Verona (1972), Where's Charley (1975), as Mack the Knife in The Threepenny Opera (1977), and in the Fellini-inspired Nine (1982).
The stage successes led to his film debut in The Organization (1971) starring opposite Sidney Poitier. In the early 1980s, Juliá was invited to join Francis Ford Coppola's Zoetrope Studios company and appeared in One From the Heart (1982).
Although he never became a major film star, Juliá had notable dramatic and comic roles in a number of films and made-for-TV-movies. In Kiss of the Spider Woman (1985), he played a passionate political prisoner, and in Romero (1989) he played the Salvadoran Archbishop Oscar Romero. In the popular two Addams Family movies, Juliá played Gomez Addams.
In 1993 he was diagnosed with cancer, but Juliá kept on acting,creating one of his most memorable roles as Brazilian rainforest activist Chico Mendez in The Burning Season (1994), for which he posthumously won a Golden Globe and an Emmy Award.
On October 16, 1994, a few days before his last movie, Street Fighter, was finished, Juliá suffered a stroke in his New York City apartment and fell into a coma. He died eight days later at age 54. His body was flown back to Puerto Rico where he was given a state funeral attended by thousands.
Movie reviewer Leonard Maltin said of him: "Droopy-eyed, dark, and suavely handsome, this extremely versatile actor was one of the most respected stage performers of his generation."