Alexander Scourby was born in Brooklyn, New York on November 13, 1913, to Constantine Nicholas Scourby, a successful restaurateur, wholesale baker and sometime investor in independent motion-pictures, and Betsy Scourby (née Patsakos), a homemaker, both of whom were immigrants from Greece.

Upon graduation from high school in 1931, Scourby, not yet having abandoned the prospect of a writing career, entered West Virginia University at Morgantown to study journalism. During his first semester he joined the campus drama group and played a minor role in A.A. Milne's comedy Mr. Pim Passes By. In February 1932, as he was beginning his second semester, his father died, and he left the university to help run the family's pie bakery in Brooklyn.

Scourby is credited as Hamlet's father the King (as spirit) on the 19 September 1936 CBS radio program "Columbia Workshop" directed by Orson Welles, and by the early 1940s he was playing running parts in five of the serial melodramas, popularly known as soap operas, including Against the Storm, in which he replaced Arnold Moss for two years. He narrated Andre Kostelanetz' musical show for a year, using the pseudonym Alexander Scott. At the request of sponsors, his voice was heard on many dramatic shows, including NBC's Sunday program The Eternal Light (with which he was to remain, despite heavy commitments elsewhere, through the 1950s). On Superman, his was the voice of the title character's father in the one program devoted to the character's origins. During World War II, Scourby's broadcasts were beamed abroad in Greek and English for the Office of War Information. At the time, a Writer in Variety (May 16, 1962) described the quality of Scourby's voice as "the kind of resonance closely associated by listeners with big time radio."

After a successful audition in the spring of 1937, Scourby was cast in a small part in a recording of Antony and Cleopatra. During the following summer he was, again, the player king in a production of Hamlet in Dennis, Massachusetts that featured Eva Le Gallienne. When he returned to audition for the American Foundation for the Blind later in the year he was told that the company of actors was "filled" but that he might record a novel if he wished. "That was the beginning of it," he recalled years later, adding, "The recordings for the blind are perhaps my greatest achievement. Most of the things I look back at in the theater were either insignificant parts in great plays or good parts in terrible plays. So it really doesn't amount to anything. Whereas I have recorded some great books. The greatest one being the Bible."

Scourby kept his hand in the theater by doing summer stock and a wide variety of other seasonal productions. In Maurice Evans' production of Hamlet, which opened at the St. James Theatre in New York on October 12, 1938 and ran for ninety-six performances, Scourby played Rosencrantz. Later in the same season he appeared with Evans in Henry IV, Part 1 as the Earl of Westmoreland. The following year, he toured with Evans in Richard II as one of the hirelings of the king. He returned to Broadway years later in late 1946, replacing Ruth Chatterton as the narrator in Ben Hecht's A Flag Is Born, a one-act, dramatic pageant in which Marlon Brando had one of his early stage roles. The play was produced by the American League for a Free Palestine, at the Alvin Theatre. On December 22, 1947, he opened with John Gielgud in Rodney Ackland's dramatization of Crime and Punishment at the National Theatre in New York. He was a co-founder of New Stages, a drama company that went into operation in a small theater on Bleecker Street in Greenwich Village during the 1947-48 season. During its two-year existence, the company presented works by such artists as Federico García Lorca (Blood Wedding), Edward Caulfield (Bruno and Sidney) and two plays by Jean-Paul Sartre.

Scourby and Lori von Eltz were married on May 12, 1943. Von Eltz was the daughter of motion-picture actor Theodor von Eltz, and was well known as the Actress Lori March. The couple had a daughter, Alexandra, born on March 27, 1944. Scourby had no political affiliation nor any specific religious affiliations, though he was baptized in the Greek Orthodox tradition and his marriage to von Eltz occurred in an Episcopal chapel.

In Sidney Kingsley's Detective Story, which opened at the Hudson Theatre on March 23, 1949 and ran for a year and eight months, Scourby played Tami Giacoppetti, the tough racketeer. Almost immediately after Detective Story closed, Scourby began rehearsing another Kingsley role on Broadway, that of Ivanoff, the old Bolshevik friend of Rubashov in Darkness at Noon, a dramatization of Arthur Koestler's novel. The play opened at the Alvin Theatre on January 13, 1951, with Claude Rains playing Rubashov, and ran for 163 performances. When the Theatre Guild revived George Bernard Shaw's Saint Joan later in the same year, with Uta Hagen in the title role, Scourby was cast as Peter Cauchon, the Bishop of Beauvais. The play was presented at the Cort Theatre from October 4, 1951 to February 2, 1952.

Scourby was the first person to record the King James Bible issued on long-play records in the 1950s. He originally narrated the Old and New Testament for the American Foundation for the Blind. The project required more than four years before it was completed in 1953. The original goal was to produce a clean, clear recording for visually impaired listeners. The American Bible Society distributed the recordings as The Talking Bible, a set of 169 LP records with a running time of 84.5 hours.

Scourby first appeared on screen opposite Glenn Ford in Affair in Trinidad (Columbia, 1952) and The Big Heat (Columbia, 1953). He appeared again with Glenn Ford in Ransom! (MGM, 1956), later to be remade with Mel Gibson and Gary Sinise. Scourby played Dr. Mikhail Andrassy in The Shaggy Dog (1959). "None of the pictures I've done have been really important or very good", Scourby later said, "with the exception—and it is debatable—of Giant (Warner Brothers, 1956)". In the film version of Edna Ferber's novel Scourby played Polo, the old Mexican ranch foreman. He later had roles in The Big Fisherman (Buena Vista, 1959), Seven Thieves (1960), The Devil at 4 O'Clock (1961) and The Executioner (1970). During these extremely busy years, Scourby, who had been living with his wife and child in an apartment near Columbia University in New York City, bought a home in Beverly Hills, California. Calls for Scourby to work in New York, however, soon made the Beverly Hills residence as much a commutation point as a home.

Back on the New York stage, Scourby played Rakitin in Emlyn Williams' adaptation of Turgenev's A Month in the Country and Peter Cauchon in Siobhán McKenna's interpretation of Saint Joan, both presented at the Off-Broadway Phoenix Theatre in 1956. Again at the Phoenix, he played King Claudius in Hamlet in the spring of 1961, bringing to the role, as Howard Taubman noted in the New York Times (March 17, 1961), the appropriate "fret of fear and decay."

In 1963, Scourby was given the featured role of Gorotchenko, the Communist commissar who stalks a White Russian noble couple fleeing the Revolution, in Tovarich, a Broadway musical by Lee Pockriss and Anne Croswell, based on the comedy by Robert E. Sherwood and Jacques Deval. The musical opened at the Broadway Theatre on March 18, 1963, with Vivien Leigh and Jean-Pierre Aumont as Scourby's prey. "The signal tribute to Alexander Scourby...", critic Norman Nadel wrote in his review in the New York World-Telegram and Sun (April 2, 1963), "was the hearty hissing opening night as he strolled on stage. In polished villainy, he has no peer". Shortly after Tovarich closed, on November 9, 1963, after 264 performances, Scourby began rehearsals in Los Angeles for a Theatre Group presentation of Anton Chekhov's The Sea Gull, in which he starred with Jeanette Nolan for forty performances, beginning on January 10, 1964.

With the advent of cassette tape Technology in the 1970s, a number of companies began selling copies of the 1950 Scourby recordings without permission, assuming that they were in public domain. In the 1980s, a Florida company, Neva Products, sought to sell these recordings via TV direct-response advertisements. Prior to doing this however, Neva commissioned a law firm to research whether or not the recordings were in the public domain. The legal opinion came back that they were not in the public domain and that certain rights were associated with the recordings that could be protected. Based upon this legal opinion, Neva Products contacted Scourby and negotiated a non-exclusive license agreement and agreed to pay him a royalty on all sales. The television promotion went very well. However, some companies continued marketing the recordings without authorization, even though they were contacted by Neva informing them that the recordings were still under copyright and to cease and desist.

Scourby produced another recording of the King James Bible for The Episcopal Radio and TV Foundation (ERTF) in 1972 on the condition that they would only be used in the Episcopal Community and only for non-profit purposes. When this recording began to be commercially exploited out in the general market as Scourby's latest narration, in 1986, Neva, with Scourby's estate, jointly sued Episcopal Radio and TV Foundation and Christian Duplication Inc. (CDI). CDI improperly purchased the recordings for commercial exploitation and refused to stop selling them after being notified by both Neva and the Estate of Alexander Scourby. At a 1989 Federal Jury Trial, the jury found both ERTF and CDI had breached their contract with Alexander Scourby. The jury awarded substantial damages to Neva Products and the Estate of Alexander Scourby and also awarded the rights to the 1970s recordings to Neva Products and the Estate of Alexander Scourby. The verdict forced ERTF, which was not officially part of the Episcopal Church, into bankruptcy.

Neva Products then negotiated another exclusive license agreement with Scourby in 1984, wherein Neva commenced lawsuits against numerous companies to stop them from selling the recordings without proper authorization. Neva was successful in this effort. One of the biggest organizations to be sued was The Christian Booksellers Association (CBA) from Colorado Springs, Colorado. They were sued because they permitted companies to illegally sell the Scourby recordings at the annual CBA convention, even after having been notified that those companies were not authorized to do so. Neva prevailed in that lawsuit. CBA was required to pay substantial financial damages for the violation.

Scourby died of a heart attack on February 22, 1985 in Newtown, Connecticut, aged 71. His widow died in 2013.

It took Neva Products approximately 5 years to stop all of the unauthorized selling of the Scourby recordings, but finally in 1990 they were successful. In 1990, Neva transferred their rights in the recordings to Litchfield Associates, and in 1991, Litchfield bought all rights, titles, and interests, including the copyrights from the estate of Alexander Scourby. The copyrights have a date of 1991. Litchfield continues to this day to market the Scourby recordings worldwide through various license agreements and online. Scourby's recordings of the Holy Bible are still among the most popular religious recordings available today.

Reared in Brooklyn, Scourby was a member of a Boy Scout troop and later became a cadet with the 101st National Guard Cavalry Regiment. He attended public and private schools in Brooklyn, spending summer vacations in New Jersey, Upstate New York, and at a cousin's home in Massachusetts. Dismissed from Polytechnic Prep School, he finished his secondary education at Brooklyn Manual Training High School which he described as "an ordinary high school that had an awful lot of shop." Scourby was a co-editor of the magazine and yearbook, and he envisioned a career in writing, though he later came to realize that writing was, for him, "absolutely the most painful thing in the world" and also that he "could never meet a deadline," whereas he found the reading aloud of plays easy and enjoyable. Encouraged by some of his teachers, he began to turn his attention to acting. He made his stage debut with the high school's dramatic society, as the Juvenile in Augustin MacHugh's The Meanest Man in the World.