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.
Oue became music director of the Greater Boston Youth Symphony Orchestras in 1982, a post he held until 1989.
After a 1997 tour with the NDR Radiophilharmonie Hanover, Oue was appointed its principal conductor in September 1998.
Oue made his debut at the Bayreuth Festival in 2005, conducting Tristan und Isolde.