In this paper we study Lagrangian Floer theory on toric manifolds from the
point of view of mirror symmetry. We construct a natural isomorphism between
the Frobenius manifold structures of the (big) quantum cohomology of the toric
manifold and of Saito's theory of singularities of the potential function
constructed in \cite{fooo09} via the Floer cohomology deformed by ambient
cycles. Our proof of the isomorphism involves the open-closed Gromov-Witten
theory of one-loop.