Robert Arthur was born on November 10, 1909, on the island of Corregidor in the Philippines, where his father was serving as an officer in the United States Army. For the first two years of his college career, he attended William and Mary College, and then transferred to the University of Michigan, from which he received a B.A. in English and an M.A. in Journalism.

In 1931, Arthur moved to New York City where he wrote mysteries, fantasies, and horror stories for pulp magazines throughout the 1930s. His work from those years appeared in Weird Tales, Amazing Stories, Detective Fiction Weekly, Argosy Weekly, Detective Story Magazine, Collier's, Bluebook, and Black Mask, among many other magazines.

Later, with his partner David Kogan, Arthur co-wrote and produced a radio show called The Mysterious Traveler that aired on the Mutual Broadcasting System between 1944 and 1952 and that won an Edgar Award for Best Radio Drama from The Mystery Writers of America in 1953. In 1946 he married fellow writer Joan Vatsek, and in 1953 their daughter Elizabeth Arthur was born.

In 1959, Arthur moved to Hollywood where he worked in television, writing scripts for The Twilight Zone and working as a story editor, show runner, and scriptwriter for Alfred Hitchcock's TV show, Alfred Hitchcock Presents. He also started to ghost-edit a series of "Alfred Hitchcock" anthologies for adults and children, and later edited and published two collections of his own short stories, entitled Ghosts and More Ghosts and Mystery and More Mystery.

In 1963, Arthur left Hollywood and moved to Cape May, New Jersey, where he created The Three Investigators, a mystery book series for young people. The Secret of Terror Castle and The Mystery of the Stuttering Parrot were published in 1964 by Random House, and Arthur wrote eight more Three Investigators novels before his early death in Philadelphia, Pennsylvania, on May 2, 1969.

After his death, his publisher arranged for other writers to continue writing stories based on his characters and setting. Three Investigators books were published in Australia, Bangladesh, India, Indonesia, Pakistan, Thailand, Denmark, Italy, Lithuania, Poland, Portugal, and Slovakia, as well as in France, Germany, Japan, the United Kingdom, and throughout the Spanish-speaking world. By the time the last English-language-original Three Investigators book was published in the late 1980s, there were forty-three titles, some of which had been translated into over twenty languages.

Robert Arthur's own ten novels are being reissued in English, by Hollow Tree Press, on the 60th anniversary of the first publication of The Secret of Terror Castle, and his daughter, Elizabeth Arthur, a novelist and memoirist, is collaborating with her husband Steven Bauer on a rebooted, contemporary Three Investigators series.