Weibel studied physics and mathematics at the University of Michigan, earning bachelor's degrees in both subjects in 1972. He was awarded a master's degree by the University of Chicago in 1973 and achieved his doctorate in 1977 under the supervision of Richard Swan (Homotopy in Algebraic K-Theory). From 1970 to 1976 he was an "Operations Research Analyst" at Standard Oil in Indiana, and spent 1977–78 at the Institute for Advanced Study. In 1978 he became an assistant professor at the University of Pennsylvania and in 1980 an assistant professor at Rutgers University, where he was promoted to professor in 1989.
He joined Vladimir Voevodsky and Markus Rost in proving the (motivic) Bloch–Kato conjecture (2009). It is a generalization of the Milnor conjecture of algebraic K-theory, which was proved by Voevodsky in the 1990s. He was a visiting professor in 1992 at the University of Paris and 1993 at the University of Strasbourg. Since 1983 he has been an editor of the Journal of Pure and Applied Algebra.
In 2014, he became a Fellow of the American Mathematical Society.
- With Eric Friedlander, An overview over algebraic K-theory, in Algebraic K-theory and its applications, World Scientific 1999, pp. 1–119 (1997 Trieste Lecture Notes)
- The K-Book, an introduction to algebraic K-theory
- With Carlo Mazza, Vladimir Voevodsky Lectures on Motivic Cohomology, Clay Monographs in Mathematics, American Mathematical Society 2006
- An introduction to homological algebra, Cambridge University Press 1994
- The proof of the Bloch-Kato conjecture, Trieste Lectures 2007, ICTP Lecture Notes Series 23 (2008), 277–305
- The norm residue isomorphism theorem, Journal of Topology, Volume 2, 2009, pp. 346–372
- List of Fellows of the American Mathematical Society, retrieved 2014-12-17
- The original article was a Google translation of the corresponding article in German Wikipedia.