  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 all-orders
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 $d\sigma/dy dQ_T$ 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> \simeq 0.18 m_h + 18 $~GeV. We provide analogous results
for $Z$ boson production, for which we compute $<Q_T> \simeq 25$ GeV. The
harder transverse momentum distribution for the Higgs boson arises because
there is more soft gluon radiation in Higgs boson production than in $Z$
production.
