Redtenbacher, son of an ironmonger from Steyr, first went through an apprenticeship in commerce and accounting. After a short interlude as technical illustrator in the "Baudirektion" (building authority) in Linz, he attended the Polytechnikum in Vienna from 1825 until 1829. He stayed there until 1834 as an assistant to Johann Arzberger. In 1835, he accepted an invitation to become a professor at the Höhere Industrieschule in Zürich, where he taught mathematics and geometry. In 1841 he finally became professor in mechanics and mechanical engineering at the Polytechnikum Karlsruhe, and as its director between 1857 and 1862, he transformed it into a school of international standing.
Redtenbacher is regarded as the founder of scientific mechanical engineering. Working at the Polytechnikum Karlsruhe, he added a mathematical foundation to the previously empirical teaching. His students include such outstanding engineers as Karl Benz, Franz Reuleaux and Emil Škoda.