The Higgs boson production cross section at pp and p̄p colliders is calculated at next-to-next-to-leading order (NNLO) in QCD. The perturbative expansion of the production cross section is found to be well behaved, with reduced scale dependence compared to the next-to-leading order (NLO) result. This provides confidence in the reliability of the prediction. An error in the NNLO correction to Drell-Yan production is also reported. Gluon fusion is the most important production channel for Higgs discovery at the LHC. The Higgs boson should manifest itself in the reaction pp → H(→ γγ) + X, where a signal should emerge on top of a very smooth, measurable γγ background. At the Tevatron, the focus for Higgs discovery is in associated production modes like W/Z + H and t̄t + H. In a mass window around the WW threshold, however, gluon fusion is important. NNLO corrections to the process gg → H have been evaluated in the heavy top limit and the approximation of soft gluon radiation. The partonic cross section is expanded in (1 - x), where x = M_H²/ŝ. The expansion includes terms up to (1 - x)^{16}. The authors of Ref. [4] evaluated the coefficient c_{03}^{(2)} at NNLO, which was included in the final results of Refs. [2, 3]. However, the unknown sub-leading terms c_{0i}^{(2)} with i ≤ 2 were treated differently by Refs. [2] and [3], leading to significant deviations in the numerical results. The current letter reports the analytical evaluation of the coefficients c_{ik}^{(2)} with k = 0, ..., 3 and l ≥ 0. The authors found an error in the NNLO Drell-Yan calculation of Ref. [5]. The correct result is given at the end of the next section. The calculation assumes all quark masses to vanish except for the top quark mass, and neglects all electro-weak couplings. The Higgs boson can couple to gluons only via a top quark loop. The effective Lagrangian is given, and the Wilson coefficient C₁(α_s) is calculated up to the order required here. The Feynman diagrams to be evaluated for hadronic collisions at NNLO include two-loop virtual diagrams for gg → H, one-loop single real emission diagrams for gg → Hg, gq → Hq, and q̄q → Hg, and tree-level double real emission diagrams for various processes. The coefficients a^{(2)} and b_{k}^{(2)} in Eq. (1) are determined by the gg sub-process only, while the c_{lk}^{(2)} receive contributions from all sub-processThe Higgs boson production cross section at pp and p̄p colliders is calculated at next-to-next-to-leading order (NNLO) in QCD. The perturbative expansion of the production cross section is found to be well behaved, with reduced scale dependence compared to the next-to-leading order (NLO) result. This provides confidence in the reliability of the prediction. An error in the NNLO correction to Drell-Yan production is also reported. Gluon fusion is the most important production channel for Higgs discovery at the LHC. The Higgs boson should manifest itself in the reaction pp → H(→ γγ) + X, where a signal should emerge on top of a very smooth, measurable γγ background. At the Tevatron, the focus for Higgs discovery is in associated production modes like W/Z + H and t̄t + H. In a mass window around the WW threshold, however, gluon fusion is important. NNLO corrections to the process gg → H have been evaluated in the heavy top limit and the approximation of soft gluon radiation. The partonic cross section is expanded in (1 - x), where x = M_H²/ŝ. The expansion includes terms up to (1 - x)^{16}. The authors of Ref. [4] evaluated the coefficient c_{03}^{(2)} at NNLO, which was included in the final results of Refs. [2, 3]. However, the unknown sub-leading terms c_{0i}^{(2)} with i ≤ 2 were treated differently by Refs. [2] and [3], leading to significant deviations in the numerical results. The current letter reports the analytical evaluation of the coefficients c_{ik}^{(2)} with k = 0, ..., 3 and l ≥ 0. The authors found an error in the NNLO Drell-Yan calculation of Ref. [5]. The correct result is given at the end of the next section. The calculation assumes all quark masses to vanish except for the top quark mass, and neglects all electro-weak couplings. The Higgs boson can couple to gluons only via a top quark loop. The effective Lagrangian is given, and the Wilson coefficient C₁(α_s) is calculated up to the order required here. The Feynman diagrams to be evaluated for hadronic collisions at NNLO include two-loop virtual diagrams for gg → H, one-loop single real emission diagrams for gg → Hg, gq → Hq, and q̄q → Hg, and tree-level double real emission diagrams for various processes. The coefficients a^{(2)} and b_{k}^{(2)} in Eq. (1) are determined by the gg sub-process only, while the c_{lk}^{(2)} receive contributions from all sub-process