A former Army major was sentenced to a 17½-year prison term on corruption charges in Wednesday in San Antonio, signaling the beginning of the end of a far-reaching Iraq War corruption probe.

As part of the probe, a growing cadre of career soldiers has confessed to siphoning millions of dollars from defense contracts in Iraq and Kuwait. The investigation into their spree already has led to the indictments of five U.S. military officers, with another dozen expected to follow.

U.S....