  Quantum teleportation (QT) serves as one of the building blocks of the
current state information science and technology which necessitates proper
characterization of the resources yielding QT. While entanglement is known to
be the basic requirement to achieve QT, condition of sufficiency for QT still
remains an open question. Here, we provide an analytic proof that in the case
of Gaussian entangled resources, in general, Einstein-Podolsky-Rosen (EPR)
correlation is {\em sufficient for QT}. For a relatively restricted set of
Gaussian states we provide even a tighter condition that EPR correlation is
{\em both necessary and sufficient for QT}. Our results, in turn, provide a
complete characterization of the resources required for QT.
