We study the collapse of rapidly rotating supermassive stars that may have formed in the early Universe. By self-consistently simulating the dynamics from the onset of collapse using three-dimensional general-relativistic hydrodynamics with fully dynamical spacetime evolution, we show that seed perturbations in the progenitor can lead to the formation of a system of two high-spin supermassive black holes, which inspiral and merge under the emission of powerful gravitational radiation that could be observed at redshifts z is approximately equal or > to 10 with the DECIGO or Big Bang Observer gravitational-wave observatories, assuming supermassive stars in the mass range 10(4)-10(6)M[symbol: see text]. The remnant is rapidly spinning with dimensionless spin a*=0.9. The surrounding accretion disk contains ~10% of the initial mass.