Cook was born in 1903 in San Francisco, California, the son of Elisha Vanslyck Cook Sr., a pharmacist, and grew up in Chicago. He first worked in theater lobbies selling programs, but by the age of 14 he was already performing in vaudeville and stock. As a young man, he traveled and honed his acting skills on stages along the East Coast and in the Midwest before arriving in New York City, where in 1926 he debuted on Broadway in Hello, Lola. Some other Broadway productions in which Cook performed were Henry-Behave (1926), Kingdom of God (1928), Her Unborn Child (1928), Many a Slip (1930), Privilege Car (1931), Lost Boy (1932), Merry-Go-Round (1932), and Chrysalis (1932). Then, in 1933, Eugene O'Neill cast him in the role of Richard Miller in his play Ah, Wilderness, which ran on Broadway for two years. Cook continued to appear on stage during the remainder the 1930s; and although his acting career after that focused increasingly on films and then on television roles, he periodically returned to Broadway, where as late as 1963 he performed as Giuseppe Givola in Bertolt Brecht's play The Resistible Rise of Arturo Ui.

In 1930, Cook traveled to California, where he made his film debut in Hollywood's version of the play Her Unborn Child, a motion picture directed by Albert Ray and produced by Windsor Picture Plays Inc. After several subequent small roles and uncredited parts in other films, he began a long period playing weaklings or sadistic losers and hoodlums, who in the plots were usually murdered, either being strangled, poisoned or shot. Hollywood's most established fall guy for many years, he made a rare appearance in a cameo role in the 1941 slapstick comedy Hellzapoppin', performing as a Screenwriter. In Universal's Phantom Lady (1944), he portrays a slimy, intoxicated nightclub-orchestra Drummer to memorable effect. He also had a substantial, though uncredited role as Bobo in the 1953 film noir production I, the Jury.

Elisha Cook was officially married three times, the first time to Actress and New York native Mary Lou (née Dunckley) Cook from 1928 until their divorce on November 4, 1941. He then married Illinois native Elvira Ann (Peggy) McKenna in 1943. The couple were married for 25 years until they formally divorced in Inyo County, California, in February 1968. Peggy and Elisha, however, remarried just short of four years later, on December 30, 1971. Their second marriage lasted another 19 years, until Peggy's death on December 23, 1990. Various references about Cook state that he had no children from his marriages; yet, his army enlistment record of 1942 documents his marital status as "Divorced, with dependents," which suggests he may have had a child or children with his first wife. With respect to his living arrangements in California, he resided for many years in Bishop, although he typically spent his summers at Lake Sabrina in the Sierra Nevada. According to John Huston, who in 1941 directed him in The Maltese Falcon:

With regard to Cook's military Service during World War II, he enlisted at the age of 38 in the United States Army on August 15, 1942, in Los Angeles, California. According to his enlistment record he stood 5-feet-5-inches tall and weighed 123 pounds. Cook's military record also documents that his highest level of education by that time was his completion of "3 years of high school". Many online references, however, state that he had attended "St. Albans College", "The Chicago Academy of Dramatic Art", and "The Chicago Academy of Fine Arts", which, it should be noted, had been renamed the Art Institute of Chicago in 1882. Those same references, though, do not provide any dates when Cook reportedly took classes at or graduated from those cited institutions.

Cook appeared on a wide variety of American television series from the early 1950s to the late 1980s. He played a private detective, Homer Garrity, in an episode of Adventures of Superman television series titled "Semi-Private Eye," airing for the first time on January 16, 1954. That same year, on April 12, he guest-starred on NBC's The Dennis Day Show. In 1960, he was cast in the episode "The Hermit" of the ABC sitcom The Real McCoys with Walter Brennan. He appeared too in 1960 as Jeremy Hake in the episode "The Bequest" of the ABC western series The Rebel, which starred Nick Adams. He also portrayed the character Gideon McCoy in the 1966 episode "The Night of the Bars of Hell" on The Wild Wild West. He performed as well in the second episode of ABC's crime drama The Fugitive.

Cook made two guest appearances on the CBS courtroom drama series Perry Mason. In 1958, he played Art Crowley in "The Case of the Pint-Sized Client", and in 1964 he played Reelin' Peter Rockwell in "The Case of the Reckless Rockhound". Cook portrayed Lawyer Samuel T. Cogley in the Star Trek 1967 episode "Court Martial", Isaac Isaacson on the Batman television series, Weasel Craig in Salem's Lot, and later had a long-term recurring role as Honolulu crime lord "Ice Pick" on CBS's Magnum, P.I. He appeared too in The Bionic Woman episode "Once a Thief" in 1977.

Cook died of a stroke at age 91, on May 18, 1995, at a nursing home in Big Pine, California. He was the last surviving member of the main cast of The Maltese Falcon.