  This Letter proposes a solution of the Vacuum Energy and the Cosmological
Constant (CC) paradox based on the Zel'dovich's ansatz, which states that the
observable contribution to the vacuum energy density is given by the
gravitational energy of virtual particle-antiparticle pairs, continually
generated and annihilated in the vacuum state. The novelty of this work is the
use of an ultraviolet cut-off length based on the Holographic Principle, which
is shown to yield current values of the CC in good agreement with experimental
observations.
