  We present the explicit de Sitter supergravity action describing the
interaction of supergravity with an arbitrary number of chiral and vector
multiplets as well as one nilpotent chiral multiplet. The action has a
non-Gaussian dependence on the auxiliary field of the nilpotent multiplet,
however, it can be integrated out for an arbitrary matter-coupled supergravity.
The general supergravity action with a given Kahler potential $K$,
superpotential $W$ and vector matrix $f_{AB}$ interacting with a nilpotent
chiral multiplet consists of the standard supergravity action defined by $K$,
$W$ and $f_{AB}$ where the scalar in the nilpotent multiplet has to be replaced
by a bilinear combination of the fermion in the nilpotent multiplet divided by
the Gaussian value of the auxiliary field. All additional contributions to the
action start with terms quartic and higher order in the fermion of the
nilpotent multiplet. These are given by a simple universal closed form
expression.
