Higgs bosons can be searched for in the channels p (p) over bar /pp --> t (
t) over barH + X at the Fermilab Tevatron and the Cern Large Hadron Collide
r (LHC). We have calculated the QCD corrections to these processes in the s
tandard model at next-to-leading order. The higher-order corrections reduce
the renormalization and factorization scale dependence considerably and st
abilize the theoretical predictions for the cross sections. At the central
scale mu = (2m(t) + M-H)/2 the properly defined K factors are slightly belo
w unity for the Tevatron (K similar to 0.8) and slightly above unity for th
e LHC (K similar to 1.2).