The diversification of complex animal life during the Cambrian Period (541-485.4 Ma) is thought to have been contingent on an oxygenation event sometime during ~850 to 541 Ma in the Neoproterozoic Era. Whilst abundant geochemical evidence indicates repeated intervals of ocean oxygenation during this time, the timing and magnitude of any changes in atmospheric pO2 remain uncertain. Recent work indicates a large increase in the tectonic CO2 degassing rate between the Neoproterozoic and Paleozoic Eras. We use a biogeochemical model to show that this increase in the total carbon and sulphur throughput of the Earth system increased the rate of organic carbon and pyrite sulphur burial and hence atmospheric pO2. Modelled atmospheric pO2 increases by ~50% during the Ediacaran Period (635-541 Ma), reaching ~0.25 of the present atmospheric level (PAL), broadly consistent with the estimated pO2 > 0.1-0.25 PAL requirement of large, mobile and predatory animals during the Cambrian explosion.