  The full gluon propagator relevant for the description of the truly
non-perturbative QCD dynamics, the so-called intrinsically non-perturbative
gluon propagator has been derived in our previous work. It explicitly depends
on the regularized mass gap, which dominates its structure at small gluon
momentum. It is automatically transversal in a gauge invariant way. It is
characterized by the presence of severe infrared singularities at small gluon
momentum, so the gluons remain massless, and this does not depend on the gauge
choice. In this paper we have shown how precisely the renormalization program
for the regularized mass gap should be performed. We have also shown how
precisely severe infrared singularities should be correctly treated. This
allowed to analytically formulate the exact and gauge-invariant criteria of
gluon and quark confinement. After the renormalization program is completed,
one can derive the gluon propagator applicable for the calculation of physical
observables processes, etc., in low-energy QCD from first principles.
