  We compute the next-to-next-to-leading order (NNLO) QCD correction to the
total cross-section for the reaction gg \to t\bar t + X. Together with the
partonic channels we computed previously, the result derived in this letter
completes the set of NNLO QCD corrections to the total top pair production
cross-section at hadron colliders. Supplementing the fixed order results with
soft-gluon resummation with next-to-next-to-leading logarithmic accuracy we
estimate that the theoretical uncertainty of this observable due to unknown
higher order corrections is about 3% at the LHC and 2.2% at the Tevatron. We
observe a good agreement between the Standard Model predictions and the
available experimental measurements. The very high theoretical precision of
this observable allows a new level of scrutiny in parton distribution functions
and new physics searches.
