We have derived a primordial helium abundance of Yp=0.2477+/-0.0029, based on new atomic physics computations of the recombination coefficients of He I and of the collisional excitation of the H I Balmer lines together with observations and photoionization models of metal-poor extragalactic H II regions. The new atomic data increase our previous determination of Yp by 0.0086, a very significant amount. By combining our Yp result with the predictions made by the standard big bang nucleosynthesis model, we find a baryon-to-photon ratio, η, in excellent agreement both with the η-value derived by the primordial deuterium abundance value observed in damped Lyα systems and with the one obtained from the WMAP observations.