  We compute the next-to-leading order virtual QCD corrections to Higgs pair
production via gluon fusion. We present analytic results for the two-loop
contributions to the spin-0 and spin-2 form factors in the amplitude. The
reducible contributions, given by the double-triangle diagrams, are evaluated
exactly while the two-loop irreducible diagrams are evaluated by an asymptotic
expansion in heavy top quark mass up to and including terms of
$\mathcal{O}(1/m_t^8)$. Assuming that the finite top-quark mass effects are of
similar size in the entire range of partonic energies we estimate that mass
effects can reduce the hadronic cross section by at most $10\%$.
