Edward Ernest Sauter was born December 2, 1914, in Brooklyn, and grew up in Nyack, New York, in Rockland County, where a schoolteacher named Gertrude Goldstein spotted his musical talent at age nine and arranged for him to play trumpet with the high school band and take advanced lessons; she also drove him into the city to perform with the Columbia Teachers College symphonic orchestra. Before graduating in 1932 he was already leading his own dance band, "Eddie Sauter and His Eight Aces," broadcasting locally on WCOH, and later that year he co-formed the Dale-Sauter Orchestra with pianist Jack Dailey, which played Manhattan's Empire Room. He went on to study at Columbia University and Juilliard, working with composers Stefan Wolpe, Bernard Wagenaar, and Louis Gruenberg, a classical grounding that would set him apart from most of his big-band arranging peers.

Sauter broke into the profession as a trumpeter with the Charlie Barnet Orchestra before joining Red Norvo's band in the mid-1930s, where he shifted from playing to writing full-time. His arrangements for Norvo's xylophone and vocalist Mildred Bailey, Norvo's wife, drew notice throughout 1935-1939; a 1938 piece in The New Republic called him "a young genius," and two of the Norvo/Bailey sides he arranged reached No. 1 on the Hit Parade that year. He carried that reputation into freelance work for Artie Shaw, Tommy Dorsey, and Woody Herman, and above all for Benny Goodman's orchestra through the first half of the 1940s, where his harmonically adventurous charts ("Benny Rides Again," "Clarinet à la King," "Moonlight on the Ganges" among them) pushed dance-band writing further than almost anyone else was attempting.

Tuberculosis interrupted his career on January 1, 1942, when he was admitted to Nyack Hospital and then spent an extended recovery at Summit Park Sanatorium in nearby Pomona under Dr. Robert Yeager's care. It was during this period, at Camp Shanks in Orangeburg, New York, that he met Army bandleader Bill Finegan, the partnership that would define the next phase of his career. After the war he wrote briefly again for Shaw and Herman, then for Ray McKinley's band, before the two arrangers reconnected: in 1952 Sauter and Finegan formed the Sauter-Finegan Orchestra, signing to RCA Victor. The band became known for pushing orchestration well past standard dance-band instrumentation (by 1957 its twenty members were credited with playing some ninety different instruments between them, including oboe, harp, and kazoo), and Time magazine in 1953 called it "the most original band heard in the U.S. in years." Its biggest hit, "Doodletown Fifers" (an adaptation of the Civil War-era tune "Kingdom Coming"), took its name from Doodletown, a hamlet near Bear Mountain not far from Sauter's own Rockland County home; "Nina Never Knew," sung by Joe Mooney, and "The Moon Is Blue," sung by Sally Sweetland, were further chart entries. The band's own size worked against it financially (Sauter later said that "being popular and famous didn't always mean that you could meet your weekly payroll for such a large band"), and after ending regular touring in 1955, the orchestra disbanded in March 1957. Sauter then moved to West Germany, succeeding Kurt Edelhagen as leader of the SWF radio orchestra in Baden-Baden from 1957 to 1959, before he and Finegan reunited in the studio for further recordings, including 1962's Stereo Fantasy.

The commission that produced Sauter's most celebrated work came from tenor saxophonist Stan Getz, whom he had known since Getz's own brief stint with Goodman's band in 1945. By 1960 Getz, based in Denmark and under commercial pressure from Verve, wanted an artistic statement rather than another set of standards; he told Sauter, who was then supporting himself largely on jingles and television scoring, "I don't want any arrangements on standards, pop songs, jazz classics, or anything. I want it to be all your own original music." Sauter responded with a seven-movement suite for strings, harp, piano, and bass with no fixed rhythm section, built so Getz could improvise with and against the orchestration rather than simply solo over it. The sessions, held at Webster Hall in New York on July 14 and 28, 1961, were complicated when Getz missed the first date after his mother's death on July 13; he later overdubbed his saxophone parts onto the pre-recorded orchestral tracks by ear, relying on perfect pitch to match Sauter's charts. Verve released the album, Focus, in January 1962 with Hershy Kay conducting and Creed Taylor producing; it earned a nomination for the 1963 Grammy Award for Best Original Jazz Composition, which went instead to Vince Guaraldi's "Cast Your Fate to the Wind." Getz called it his own favorite among all his recordings.

Sauter spent his later years working across film, television, and Broadway. He wrote the score for Arthur Penn's 1965 film Mickey One, performed on record by Getz; composed the third-season theme for Rod Serling's Night Gallery and the "World Without Time" theme for the public-affairs series The Open Mind; and orchestrated roughly ten Broadway shows beginning with Milk and Honey (1961) and including The Apple Tree (1966), It's a Bird...It's a Plane...It's Superman (1966), and 1776 (1969); theater orchestrator Jonathan Tunick later recalled that "Eddie did these marvelous things, always theatrical, always effective." His 1955 Concerto for Jazz Band and Symphony Orchestra, recorded with Fritz Reiner and the Chicago Symphony Orchestra, was revived decades later by the Boston Pops under Arthur Fiedler. Sauter died of a heart attack on April 21, 1981, at Nyack Hospital, not far from the childhood home where his musical career had begun; he was posthumously inducted into the Big Band and Jazz Hall of Fame in 2003, and his manuscripts and parts are now held in an Eddie Sauter Archive at Yale University.

Sauter's classical training under Wolpe, Wagenaar, and Gruenberg, and his stated admiration for Bartók, Prokofiev, and Stravinsky, gave his big-band writing a harmonic and textural range that set him apart from most swing-era arrangers; his son Gregory has recalled Sauter's own compositional rule of thumb, that "you should always try to have three things going at once." Bandleader Glenn Miller reportedly said Sauter's writing was a decade ahead of its time, and critic George Simon suggested the music world needed twenty years to catch up with it. That reach showed up first in dissonant, structurally complex charts for Red Norvo and Benny Goodman, then in the Sauter-Finegan Orchestra's deliberately uncommercial embrace of orchestral color and novelty instrumentation, and finally in Focus, which the Penguin Guide to Jazz singled out for its "superlative" arranging and which biographer Donald L. Maggin called "the most fully realized third stream record ever made," a suite built for a soloist to work against rather than simply over. On the strength of that body of work, Sauter is usually placed in a small company of composer-arrangers who built a big band's identity around specific musicians' voices rather than interchangeable sections, alongside Duke Ellington and Gil Evans, a lineage critics have since extended to Toshiko Akiyoshi's big band writing as well.