  De Sitter supergravity describes interaction of supergravity with general
chiral and vector multiplets as well as one nilpotent chiral multiplet. The
extra universal positive term in the potential due to the nilpotent multiplet,
corresponding to the anti-D3 brane in string theory, supports de Sitter vacua
in these supergravity models. In the flat space limit these supergravity models
include the Volkov-Akulov model with a non-linearly realized supersymmetry. The
rules for constructing pure de Sitter supergravity action are generalized here
in presence of other matter multiplets. We present a strategy to derive the
complete closed form general supergravity action with a given Kahler potential
$K$, superpotential $W$ and vector matrix $f_{AB}$ interacting with a nilpotent
chiral multiplet. It has the potential $V=e^K(|F^2 |+ |DW|^2 - 3 |W|^2)$, where
$F$ is a necessarily non-vanishing value of the auxiliary field of the
nilpotent multiplet. De Sitter vacua are present under simple condition that
$|F^2|- 3|W|^2>0$. A complete explicit action in the unitary gauge is
presented.
