  We show that Weinberg's leading soft photon theorem in massless abelian gauge
theories implies the existence of an infinite-dimensional large gauge symmetry
which acts non-trivially on the null boundaries ${\mathscr I}^\pm$ of
$(d+2)$-dimensional Minkowski spacetime. These symmetries are parameterized by
an arbitrary function $\varepsilon(x)$ of the $d$-dimensional celestial sphere
living at ${\mathscr I}^\pm$. This extends the previously established
equivalence between Weinberg's leading soft theorem and asymptotic symmetries
from four and higher even dimensions to \emph{all} higher dimensions.
