The mechanism by which astrophysical jets form is an important factor in understanding the nature and evolution of phenomena such as active galactic nuclei and quasars, Galactic superluminal X-ray sources and young stellar objects. Of the many schemes proposed for jet production, only the magnetized accretion disk model of Blandford and Payne(1) seems to be applicable to all of these systems, and also offers the potential for generating the highly relativistic flows observed in some quasars(2). But the source of variation in jet morphology observed for different sources remains unclear. Here we report time-dependent numerical simulations of jet formation which show that the character and speed of the jets produced depend dramatically on whether magnetic forces dominate over gravity in the accretion disk corona. This ’magnetic switch’ is not predicted by steady-state, self-similar disk models, or by relativistic wind theory (which generally ignores the gravitational field). The effect provides a natural explanation for the existence of two known classes of extragalactic radio source and for the variation of their properties with radio luminosity. It also provides insight into protostellar and galactic microquasar systems.