A cosmological solution of the Einstein-Maxwell's field equations, corresponding to the case of a uniform (that is, covariant constant) electromagnetic field, is derived by means of simple geometrical arguments; the Riemannian manifold it corresponds to is the product of two ordinary surfaces of constant curvature, whose type and radius depend on the values of the cosmological constant and the invariants of the electromagnetic field. The world-lines of charged test particles have also a very simple geometrical meaning.