Oue began his conducting studies with Hideo Saito of the Toho Gakuen School of Music. In 1978, Seiji Ozawa invited him to spend the summer studying at the Tanglewood Music Center. While there, he met Leonard Bernstein, who became a mentor. Oue won the Tanglewood Koussevitzky Prize in 1980. He also studied under Bernstein as a conducting fellow at the Los Angeles Philharmonic Institute.
Oue became Music Director of the Greater Boston Youth Symphony Orchestras in 1982, a post he held until 1989. He was music director of the Erie Philharmonic from 1990 to 1995. He has also served as associate conductor of the Buffalo Philharmonic Orchestra. From 1995 to 2002, he was music director of the Minnesota Orchestra. During his Minnesota tenure, the orchestra saw its attendance decline from 84% to 69% in capacity. He presided over the orchestra's first tours to Europe and Japan. He also recorded 20 CDs with the Minnesota, most of which were recorded on the Reference Records label.  Oue served as Music Director of the Grand Teton Music Festival in Wyoming from 1997 to 2003.
Following a tour in 1997 with the NDR Philharmonie Hannover, Oue was subsequently appointed its principal conductor in September 1998. In 2003, he was appointed principal conductor of the Osaka Philharmonic Orchestra. Oue made his debut at the Bayreuth Festival in 2005 conducting Tristan und Isolde. He became music director of the Orquestra Simfònica de Barcelona in September 2006. He is scheduled to step down from the Barcelona post after the 2009-2010 season.
Oue's commercial recordings include Niccolò Paganini’s Violin Concerto No. 1 and Louis Spohr’s Violin Concerto No. 8 with the Swedish Radio Symphony Orchestra and Hilary Hahn for Deutsche Grammophon.
He has been professor for conducting at the Musikhochschule Hannover since 2000.
- Biography in "Respighi: Belkis, Queen of Sheba, suite, et al." Minnesota Orchestra, Eiji Oue, conductor. Sound recording :(RR-95CD)
- R.W. Apple Jr. (29 January 2000). "Where Winter's a Wonder and Smiles Are Sincere. You Betcha". New York Times. Retrieved 2009-10-02.
- "González es elegido director titular de la Sinfónica de Barcelona". La Voz de Asturias. 17 April 2009. Retrieved 2009-09-30.[permanent dead link]
- Vivien Schweitzer (29 October 2006). "A Low-Profile Name From the Past and One Known to All Today". New York Times. Retrieved 2009-09-30.
| Music Director, Grand Teton Music Festival
| Music Director, Osaka Philharmonic Orchestra
| Orquestra Simfònica de Barcelona i Nacional de Catalunya