The Earth has cooled since its formation, yet the decay of radiogenic isotopes, and in particular uranium, thorium and potassium, in the planet's interior provides a continuing heat source. The current total heat flux from the Earth to space is 44.2+/-1.0TW, but the relative contributions from residual primordial heat and radiogenic decay remain uncertain. However, radiogenic decay can be estimated from the flux of geoneutrinos, electrically neutral particles that are emitted during radioactive decay and can pass through the Earth virtually unaffected. Here we combine precise measurements of the geoneutrino flux from the Kamioka Liquid-Scintillator Antineutrino Detector, Japan, with existing measurements from the Borexino detector, Italy. We find that decay of uranium-238 and thorium-232 together contribute TW to Earth's heat flux. The neutrinos emitted from the decay of potassium-40 are below the limits of detection in our experiments, but are known to contribute 4TW. Taken together, our observations indicate that heat from radioactive decay contributes about half of Earth's total heat flux. We therefore conclude that Earth's primordial heat supply has not yet been exhausted.