We consider Higgs boson pair production via gluon fusion in hadronic collisions. We report the calculation of the transverse-momentum () distribution of the Higgs boson pair with top-quark mass () effects fully taken into account. At small values of we resum the logarithmically-enhanced perturbative QCD contributions up to next-to-leading logarithmic (NLL) accuracy. At intermediate and large values of we consistently combine resummation with the fixed-order results. After integration over , we recover the next-to-leading order (NLO) result for the inclusive cross section with full dependence on . We present illustrative numerical results at LHC energies, together with an estimate of the corresponding perturbative uncertainties, and we study the impact of the top-quark mass effects.