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By combining these calculations with measurements of the 6d and 5f hyperfine constants [C. J. Campbell et al., Phys. Rev. Lett. 106, 223001 (2011)], we determine the magnetic dipole \\mu=0.360(7)\\mu_B and the electric-quadrupole Q=3.11(6) eb moments of the 229Th nucleus. Our value for \\mu is five times more accurate and is 22% smaller than the best previous value \\mu=0.46(4) \\mu_B [S. Gerstenkorn et al., J. Phys. 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