Shelton is the President of the University of Arizona. Previously he served as the Executive Vice Chancellor and Provost of the University of North Carolina at Chapel Hill. He served as Vice Provost for Research at the University of CA, Office of the President and was responsible for building leadership among the many offices, campuses, Department of Energy (DOE) laboratories and research facilities of UC. He was responsible for developing university positions on major policy issues related to research; identifying and developing strategic responses to major research opportunities and initiatives, and providing mechanisms to facilitate them; and ensuring oversight of DOE laboratory programs and fostering research collaboration between the campuses and the national laboratories.

He received his doctorate in physics from the University of CA, San Diego in 1975, specializing in experimental condensed-matter physics. He held an appointment as Professor of Physics at the University of CA, Davis, where he also served as the Vice Chancellor for Research from 1990-96. Shelton has received numerous awards and honors, including being selected editor of the Journal of Physics and Chemistry of Solids, elected as a Fellow of the American Physical Society, and being invited to nominate for the Nobel Prize in Physics.