Originally from Galveston, Texas, Ekelund attended St. Mary's University in San Antonio, Texas, earning his B.B.A. in economics in 1962 and his M.A. in economics and history the next year. He was a member of the Order of the Barons and first worked as an instructor in economics while completing his master's degree.
He then moved to Baton Rouge, Louisiana to teach and continue his graduate work atLouisiana State University. He finished his Ph.D. in economics and political theory there in 1967. His doctoral dissertation was on Jules Dupuit, a French civil engineer and economist. Ekelund would maintain this interest in Dupuit, making him the topic of a dozen journal articles and a 1999 book, Secret Origins of Modern Microeconomics: Dupuit and the Engineers.
In 1967, after the completion of his Ph.D., Ekelund was hired by Texas A&M Universityeconomics department. He was made Professor of Economics in 1974 and remained on the faculty of the College Station, Texas school until 1979, when he moved to Auburn, Alabama to become a professor at Auburn University. Ekelund was a visiting scholar at the Hoover Institution at Stanford University and in 2003 he served as the Vernon Taylor Distinguished Visiting Professor at Trinity University in San Antonio, Texas. Ekelund is now Catherine and Edward Lowder Eminent Scholar Emeritus at Auburn University and is a policy advisor to the Heartland Institute. He is also an Independent Institute research fellow and an adjunct faculty member of the Mises Institute.