The quantum numbers of the X(3872) meson are determined to be J(PC)=1(++) based on angular correlations in B(+)→X(3872)K(+) decays, where X(3872)→π(+)π(-)J/ψ and J/ψ→μ(+)μ(-). The data correspond to 1.0 fb(-1) of pp collisions collected by the LHCb detector. The only alternative assignment allowed by previous measurements J(PC)=2(-+) is rejected with a confidence level equivalent to more than 8 Gaussian standard deviations using a likelihood-ratio test in the full angular phase space. This result favors exotic explanations of the X(3872) state.