  We prove that, for M theory or type II, generic Minkowski flux backgrounds
preserving $\mathcal{N}$ supersymmetries in dimensions $D\geq4$ correspond
precisely to integrable generalised $G_{\mathcal{N}}$ structures, where
$G_{\mathcal{N}}$ is the generalised structure group defined by the Killing
spinors. In other words, they are the analogues of special holonomy manifolds
in $E_{d(d)} \times\mathbb{R}^+$ generalised geometry. In establishing this
result, we introduce the Kosmann-Dorfman bracket, a generalisation of Kosmann's
Lie derivative of spinors. This allows us to write down the internal sector of
the Killing superalgebra, which takes a rather simple form and whose closure is
the key step in proving the main result. In addition, we find that the
eleven-dimensional Killing superalgebra of these backgrounds is necessarily the
supertranslational part of the $\mathcal{N}$-extended super-Poincar\'e algebra.
