Let $M$ be a smooth 4-manifold which admits a relatively minimal hyperelliptic genus $h$ Lefschetz fibration over $S^2$. If all of the vanishing cycles for this fibration are nonseparating curves, then we show that $M$ is a 2-fold cover of an $S^2$-bundle over $S^2$, branched over an embedded surface. If the collection of vanishing cycles for this fibration includes $\s$ separating curves, we show that $M$ is the relative minimalization of a Lefschetz fibration constructed as a 2-fold branched cover of $\cp \# (2\s+1) \cpb,$ branched over an embedded surface.