  We describe off-shell $\mathcal{N}=1$ M-theory compactifications down to four
dimensions in terms of eight-dimensional manifolds equipped with a topological
$Spin(7)$-structure. Motivated by the exceptionally generalized geometry
formulation of M-theory compactifications, we consider an eight-dimensional
manifold $\mathcal{M}_{8}$ equipped with a particular set of tensors
$\mathfrak{S}$ that allow to naturally embed in $\mathcal{M}_{8}$ a family of
$G_{2}$-structure seven-dimensional manifolds as the leaves of a
codimension-one foliation. Under a different set of assumptions, $\mathfrak{S}$
allows to make $\mathcal{M}_{8}$ into a principal $S^{1}$ bundle, which is
equipped with a topological $Spin(7)$-structure if the base is equipped with a
topological $G_{2}$-structure. We also show that $\mathfrak{S}$ can be
naturally used to describe regular as well as a singular elliptic fibrations on
$\mathcal{M}_{8}$, which may be relevant for F-theory applications, and prove
several mathematical results concerning the relation between topological
$G_{2}$-structures in seven dimensions and topological $Spin(7)$-structures in
eight dimensions.
