Welch went to the University of Montana, where he studied under the author Richard Hugo and began his writing career. Welch taught at the University of Washington and at Cornell, as well as serving on the Parole Board of the Montana Prisons Systems and on the Board of Directors of the Newberry Library D'Arcy McNickle Center.

Welch was at the University of Montana when his writing career began in earnest, leading to the creation of works that would establish his place in the Native American Renaissance literary movement.

Welch and Paul Stekler co-wrote the Emmy Award-winning American Experience documentary, Last Stand at Little Bighorn, shown on PBS. Together they also wrote the history Killing Custer: The Battle of Little Bighorn and the Fate of the Plains Indians (1994).

When Winter in the Blood was reprinted in 2007, it included an introduction by Louise Erdrich, who wrote: It "is a central and inspiring text to a generation of western regional and Native American writers, including me."

Welch died at age 62 in his home in Missoula, Montana in 2003.