Weibel studied physics and mathematics at the University of Michigan with bachelor's degrees in both subjects in 1972 and at the University of Chicago the master's degree in 1973 and his doctorate in 1977 under the supervision of Richard Swan (Homotopy in Algebraic K-Theory). From 1970 to 1976 he was "Operations Research Analyst" at Standard Oil in Indiana and in 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 and in 1989 a professor at the Rutgers University.
He joined Vladimir Voevodsky and Markus Rost proving (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.
In 1992 he was a visiting professor in Paris and 1993 in Strasbourg. From 1983 he is an editor of the Journal of Pure and Applied Algebra.
- 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
- The original article was a Google translation of the corresponding article in German Wikipedia.