  A $n$-dimensional Gorenstein toric Fano variety $X$ is called Del Pezzo
variety if the anticanonical class $-K_X$ is a $(n-1)$-multiple of a Cartier
divisor. Our purpose is to give a complete biregular classfication of
Gorenstein toric Del Pezzo varieties in arbitrary dimension $n \geq 2$. We show
that up to isomorphism there exist exactly 37 Gorenstein toric Del Pezzo
varieties of dimension $n$ which are not cones over $(n-1)$-dimensional
Gorenstein toric Del Pezzo varieties. Our results are closely related to the
classification of all Minkowski sum decompositions of reflexive polygons due to
Emiris and Tsigaridas and to the classification up to deformation of
$n$-dimensional almost Del Pezzo manifolds obtained by Jahnke and Peternell.
