Born in Brodhead, Wisconsin, Kjelland received his bachelor's degree in music education from the University of Wisconsin-Madison and his PhD from the University of Texas at Austin. After teaching instrumental music in Middleton, Wisconsin, he joined the University of Southern California faculty in 1977 as associate professor of music education and director of string development. In 1984 he became director of orchestras and coordinator of strings at California's Colburn School of Performing Arts. He moved to the University of North Texas as associate professor of music education in 1991 and came to Northwestern three years later.
Kjelland has served as a guest conductor at all-state and regional honors orchestras across the United States and as a summer string workshop instructor at such schools as the University of Wisconsin, Ohio State University, and the University of California, Los Angeles. Over the past 35 years he has garnered national acclaim for his in-service clinics and workshops in string pedagogy and orchestra development.
A past editorial board member for the Council for Research in Music Education and the American String Teachers Association, Kjelland has published more than 25 articles in journals such as American String Teacher, the Instrumentalist, and Bulletin of the Council for Research in Music Education. He wrote the textbook Orchestral Bowing: Style and Function (Alfred Publishing) and coauthored many other books, including Strictly Strings, a Comprehensive String Class Method (Alfred), Teaching Stringed Instruments: A Course of Study (R&L Education), and the three-volume Teaching Music through Performance in Orchestra (GIA Publications).