Jenne attended Washington High School in Portland, Oregon where he played football, baseball, and basketball. He later attended Washington State University, where he excelled in the pole vault. In 1920, he was a member of the United States track and field team at the 1920 Summer Olympics in Antwerp, Belgium, finishing seventh in the pole vault competition.
In 1921, Jenne tied for the individual pole vault championship at the NCAA Men's Outdoor Track and Field Championship. He was Washington State's first Olympian and is a member of the Washington State University Sports Hall of Fame.
Following the end of his athletic career, Jenne returned to Portland to coach football, basketball, baseball, and track at Washington High School. In 1928, he coached the boys' basketball team to the Oregon state championship, defeating future University of Oregon football coach Prink Callison's Medford High School team. Jenne's football teams amassed an overall 61-16-14 record with seven Portland city championships, one state championship, with only one losing season.
Jenne also served as head football and basketball coach at Pacific University. He led the Portland Interscholastic League's athletic program from 1938 until his retirement in 1965. In 1983, he was named to the Oregon Sports Hall of Fame for his achievements in coaching.
- "PIL Hall of Fame Cyber Museum: Eldon Jenne". Portland Interscholastic Hall of Fame. October 2006. Retrieved 2008-03-18.
- Pasero, George (March 28, 1993). "Deaths deplete Northwest's sports heritage". The Oregonian. p. D2.
- "OSAA Boys' Basketball Championships" (PDF). Oregon School Activities Association. Retrieved 2008-03-18.
- "Pacific University Men's Basketball 2007-08 Media Guide" (PDF). p. 27. Archived from the original (PDF) on 2008-10-07. Retrieved 2008-03-18.
- "Hall of Fame Roll of Honor Members". Oregon Sports Hall of Fame. Archived from the original on July 27, 2011. Retrieved May 24, 2011.