Precision Evaluation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi></mml:math>- and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>η

Next to the π^{0} pole, η and η^{'} intermediate states give rise to the leading singularities of the hadronic light-by-light tensor, resulting in sizable contributions to the anomalous magnetic moment of the muon a_{μ}. The strength of the poles is determined by the respective transition form factors (TFFs) to two (virtual) photons. We present a calculation of these TFFs that implements a number of low- and high-energy constraints, including the η^{(')}→γγ decay widths, η^{(')}→π^{+}π^{-}γ spectra, chiral symmetry for the η^{(')}→2(π^{+}π^{-}) amplitudes, vector-meson couplings, and asymptotic limits. Crucially, we investigate the role of the leading left-hand singularity generated by the exchange of the a_{2} tensor meson, yielding, for the first time, an estimate of the associated factorization-breaking corrections. Our final results, a_{μ}^{η pole}=14.7(9)×10^{-11} and a_{μ}^{η^{'} pole}=13.5(7)×10^{-11}, conclude a dedicated effort to evaluate the pseudoscalar-pole contributions to hadronic light-by-light scattering using dispersion relations, amounting to a combined a_{μ}^{PS poles}=91.2_{-2.4}^{+2.9}×10^{-11}.