Eddie Edwards was born in New Orleans, Louisiana, started playing violin at age 10, and took up trombone in addition at 15. He played both instruments professionally, including with the bands of Papa Jack Laine and Ernest Giardina. In addition to music Edwards played minor-league baseball and worked as an electrician.
In 1916 he was picked by Alcide Nunez to go to Chicago, Illinois to play trombone with Johnny Stein's Jass Band. With a few changes of personel this band became the famous Original Dixieland Jass Band which made the first records of jazz music in 1917.
He left the band after being drafted into the United States Army. The O.D.J.B. replaced him with Emile Christian. Edwards served in the Army from July of 1918 to March of 1919. After discharge he led a band of his own and worked in the band of Jimmie Durante before returning to the O.D.J.B.
After the break up the Original Dixieland Jazz Band, Edwards again led his own band in New York City for most of the 1920s. In the early 1930s he retired from music and ran a newspaper stand and worked as a sports coach.
He returned to music when Nick LaRocca reformed the O.D.J.B. in 1936, playing with them until 1938. He played with other bands including O.D.J.B. alumni Larry Shields, Tony Sbarbaro, and J. Russell Robinson in New York into the 1940s. He continued playing professionally irregularly until shortly before his death in New York City.
Johnny Wiggs said that while he'd heard more sophisticated trombone players, he'd never heard another trombonist who could give a band the rhythmic punch that Edwards could.