Kimball was the son of Spencer W. Kimball, a president of The Church of Jesus Christ of Latter-day Saints (LDS Church), and his wife, Camilla Eyring Kimball, and wrote notable biographies of his father. Mormon historians have described these as "well crafted" biographies.
Kimball was born in Arizona on September 23, 1930, and he suffered from polio as a child. He served as a missionary for the LDS Church in the Netherlands. He received a bachelor's degree in history and a law degree from the University of Utah. Kimball then went on to earn two further law degrees from the University of Pennsylvania.
Kimball served in several positions in the LDS Church, including bishop.
Prior to joining the faculty of BYU, Kimball was a law professor and chairman of the Curriculum Committee at the University of Wisconsin Law School. Kimball started his career as a law professor at the University of Montana, where he taught from 1956 to 1962. He was a professor at the University of Wisconsin from 1962 to 1973. He was one of the founding faculty at BYU Law School from 1973 until 1995, when he was granted emeritus status.
Kimball died in Provo, Utah on November 21, 2016 at the age of 86.
Kimball's biography of his father has been listed among "60 Significant Mormon Biographies". Lengthen Your Stride, his history of his father's church presidency, has also been widely recognized.[by whom?]
Kimball wrote an article on Henry Eyring and Harvey Fletcher published in Dialogue: A Journal of Mormon Thought. Kimball served as the editor of his father's book Faith Precedes the Miracle. Kimball was also the compiler and editor of the widely cited work, The Teachings of Spencer W. Kimball (Salt Lake City: Bookcraft, 1982).
Kimball has published an in-depth study on the 1978 Revelation on Priesthood received by his father. He has also written an article on the history of LDS Church temple admissions standards.
- Spencer W. Kimball, The Twelfth President of the Church of Jesus Christ of Latter-day Saints (with Andrew E. Kimball, Jr.), Bookcraft, 1977.
- Camilla: A Biography of Camilla Eyring Kimball. With Carolina Eyring Miner. Deseret Book, 1980.
- Ed., The Teachings of Spencer W. Kimball. Bookcraft, 1982.
- The Story of Spencer W. Kimball, A Short Man, A Long Stride. with A. E. Kimball, Jr. Bookcraft, 1985.
- Lengthen Your Stride: The Presidency of Spencer W. Kimball. Deseret Book, 2005.
- Andrew Kimball: Father of a Prophet. Deseret Book, 2011.
- Edward L. Kimball at the MLCA Database
- article from JSTOR co-authored by Kimball that mentions him being a law professor
- Edward L. Kimball, "Spencer Kimball and Recharging the Battery", Ensign, December 1993, p. 22
- Meridian Magazine bio of Kimball
-  Interview on Mormon Stories
- BYU Magazine review of Lengthen Your Stride
- Walker, Ronald W.; Whittaker, David J.; Allen, James B. (2001). Mormon History. Champaign: University of Illinois Press. p. 129. ISBN 9780252026195. Retrieved 2009-01-28.
- Carolina Eyring Miner and Edward L. Kimball. Camilla: A Biography of Camilla Eyring Kimball. (Salt Lake City: Desert Book, 1980) p. 111
- Citation of an article co-authored by Kimball
- Article by Kimball on criminal cases in Wisconsin Appellate courts
- Deseret News May 3, 1954
- Deseret News Oct. 3, 2012
- Based on gargoyle_02_1_6.pdf with added support from the author bio included with Camilla, although the later does not specify which University in Wisconsin Kimball was connected with]
- BYU Law bio of Kimball
- [https://archive.today/20120710181615/http://mormonlit.lib.byu.edu/html/biographies.html Stephen C. Biggs and Gideon O. Burton. "60 Significant Mormon Biographies." Archived Web page, listing 60 significant Mormon biographies and explaining why each is included.]
- Edward L. Kimball. "Harvey Fletcher and Henry Eyring: Men of Faith and Science." Dialogue, Vol. 15, no. 3 (1982).
- Report on Kimball's BYU Studies article
- Spencer W. Kimball and the Revelation on Priesthood
- Reference to Kimball's article in a bibliography Archived 2009-01-14 at the Wayback Machine