The orbital properties of Phoebe, one of Saturn's irregular moons, suggest that it was captured by the ringed planet's gravitational field rather than formed in situ. Phoebe's generally dark surface shows evidence of water ice, but otherwise the surface most closely resembles that of C-type asteroids and small outer Solar System bodies such as Chiron and Pholus that are thought to have originated in the Kuiper belt. A close fly-by of Phoebe by the Cassini-Huygens spacecraft on 11 June 2004 (19 days before the spacecraft entered orbit around Saturn) provided an opportunity to test the hypothesis that this moon did not form in situ during Saturn's formation, but is instead a product of the larger protoplanetary disk or `solar nebula'. Here we derive the rock-to-ice ratio of Phoebe using its density combined with newly measured oxygen and carbon abundances in the solar photosphere. Phoebe's composition is close to that derived for other solar nebula bodies such as Triton and Pluto, but is very different from that of the regular satellites of Saturn, supporting Phoebe's origin as a captured body from the outer Solar System.