Dekker was born in Brooklyn, New York City, the only child of Thomas and Grace Ecke Van Dekker. He attended Richmond Hill High School, where he appeared in stage productions. He then attended Bowdoin College, where he majored in pre-med with plans to become a doctor. On the advice of a friend, he decided to pursue acting as a career. He made his professional acting debut with a Cincinnati stock company in 1927. Within a few months, Dekker was featured in the Broadway production of Eugene O'Neill's play Marco Millions.
After a decade of theatrical appearances, Dekker transferred to Hollywood in 1937 and made his first film, 1937's The Great Garrick. He spent most of the rest of his acting career in the cinema but returned to the stage from time to time.
He replaced Lee J. Cobb as Willy Loman in the original production of Arthur Miller's Death of a Salesman, and during a five-year stint back on Broadway in the early 1960s, he played the Duke of Norfolk in Robert Bolt's A Man for All Seasons.
Dekker appeared in some 70 films from the 1930s to the 1960s, but his four famous screen roles were as a mad scientist in the 1940 horror film Dr. Cyclops, as a criminal mastermind in 1946's The Killers, as a dangerous dealer in atomic fuel in the 1955 Kiss Me Deadly, and as an unscrupulous railroad detective in Sam Peckinpah's Western The Wild Bunch, released in 1969. In 1959, he played a Texas Ranger in The Wonderful Country. He was rarely cast in romantic roles, but in the film Seven Sinners, featuring a romance between Marlene Dietrich and John Wayne, Dietrich sails off with Dekker's character at the end of the film. Dekker was an often memorable guest star – usually a villain – in numerous TV series from the 1950s through 1968, such as Rawhide, The Man From UNCLE, Mission: Impossible, Climax!, Bonanza, and I Spy. Dekker's role as Pat Harrigan in The Wild Bunch was his last screen appearance; he died over a year before it was released.