The Cambrian is the most poorly dated period of the past 541 million years. This hampers analysis of profound environmental and biological changes that took place during this period. Astronomically forced climate cycles recognized in sediments and anchored to radioisotopic ages provide a powerful geochronometer that has fundamentally refined Mesozoic–Cenozoic time scales but not yet the Palaeozoic. Here we report a continuous astronomical signal detected as geochemical variations (1 mm resolution) in the late Cambrian Alum Shale Formation that is used to establish a 16-Myr-long astronomical time scale, anchored by radioisotopic dates. The resulting time scale is biostratigraphically well-constrained, allowing correlation of the late Cambrian global stage boundaries with the 405-kyr astrochronological framework. This enables a first assessment, in numerical time, of the evolution of major biotic and abiotic changes, including the end-Marjuman extinctions and the Steptoean Positive Carbon Isotope Excursion, that characterized the late Cambrian Earth.