Born in Utah, Nebeker received an associate degree in history from Weber College, a bachelor's degree in political science from the University of Utah, and a Juris Doctor from American University.

During his law school years, Nebeker worked as a correspondence secretary in the White House.

He began his legal career in 1956 as a trial attorney in the Internal Security Division of the Department of Justice.

Two years later, he became an Assistant United States Attorney for the District of Columbia, serving from 1962 to 1969 as the Chief of the Appellate Division.

In November 2000, he retired from the U.S. Court of Appeals for Veterans Claims and served in recall status until December 20, 2021.