The regular satellites of the giant planets are believed to have finished their accretion concurrent with the planets, about 4.5 Gyr ago. A population of Saturn's small moons orbiting just outside the main rings are dynamically young (less than 10(7) yr old), which is inconsistent with the formation timescale for the regular satellites. They are also underdense ( approximately 600 kg m(-3)) and show spectral characteristics similar to those of the main rings. It has been suggested that they accreted at the rings' edge, but hitherto it has been impossible to model the formation process fully owing to a lack of computational power. Here we report a hybrid simulation in which the viscous spreading of Saturn's rings beyond the Roche limit (the distance beyond which the rings are gravitationally unstable) gives rise to the small moons. The moonlets' mass distribution and orbital architecture are reproduced. The current confinement of the main rings and the existence of the dusty F ring are shown to be direct consequences of the coupling of viscous evolution and satellite formation. Saturn's rings, like a mini protoplanetary disk, may be the last place where accretion was recently active in the Solar System, some 10(6)-10(7) yr ago.