Born in Richmond, Virginia, Moser first studied singing in Philadelphia (Curtis Institute of Music) and California (Music Academy of the West) - with Martial Singher, attended master classes with Lotte Lehmann and Gérard Souzay - before moving to Europe in 1975. There he made his debut in Graz, first as lyric tenor and Mozart interpreter. Only two years later, Moser sang for the first time at the Vienna State Opera, as Iopas in Berlioz' opera Les Troyens).
In the 1990s, Moser increasingly turned to heldentenor roles and first appeared as Lohengrin, then also as Parsifal and finally also as Tristan. In this role he celebrated an outstanding success at the side of Deborah Voigt in Vienna in spring 2003 in the new production directed by Christian Thielemann and Günter Krämer.
Moser has been an Austrian citizen since 1992.