Accretion disks around compact objects are expected to enter an unstable phase at high luminosity1. One instability may occur when the radiation pressure generated by accretion modifies the disk viscosity, resulting in the cyclic depletion and refilling of the inner disk on short timescales2. Such a scenario, however, has only been quantitatively verified for a single stellar-mass black hole3-5. Although there are hints of these cycles in a few isolated cases6-10, their apparent absence in the variable emission of most bright accreting neutron stars and black holes has been a continuing puzzle11. Here we report the presence of the same multiwavelength instability around an accreting neutron star. Moreover, we show that the variability across the electromagnetic spectrum—from radio to X-ray—of both black holes and neutron stars at high accretion rates can be explained consistently if the accretion disks are unstable, producing relativistic ejections during transitions that deplete or refill the inner disk. Such a new association allows us to identify the main physical components responsible for the fast multiwavelength variability of highly accreting compact objects.