The transverse momentum Q T distribution is computed for inclusive Higgs boson production at the energy of the CERN Large Hadron Collider. We focus on the dominant gluon-gluon subprocess in perturbative quantum chromodynamics and incorporate contributions from the quark-gluon and quark-antiquark channels. Using an impact-parameter b-space formalism, we include allorders resummation of large logarithms associated with emission of soft gluons. Our resummed results merge smoothly at large Q T with the fixed-order expectations in perturbative quantum chromodynamics, as they should, with no need for a matching procedure. They show a high degree of stability with respect to variation of parameters associated with the non-perturbative input at low Q T . We provide distributions dσ/dydQ T for Higgs boson masses from M Z to 200 GeV. The average transverse momentum at zero rapidity y grows approximately linearly with mass of the Higgs boson over the range M Z < m h < 200 GeV, < Q T >≃ 0.18m h + 18 GeV. We provide analogous results for Z boson production, for which we compute < Q T >≃ 25 GeV. The harder transverse momentum distribution for the Higgs boson arises because there is more soft gluon radiation in Higgs boson production than in Z