  Let $X$ be a compact toric K\"ahler manifold with $-K_X$ nef. Let $L\subset
X$ be a regular fiber of the moment map of the Hamiltonian torus action on $X$.
Fukaya-Oh-Ohta-Ono defined open Gromov-Witten (GW) invariants of $X$ as virtual
counts of holomorphic discs with Lagrangian boundary condition $L$. We prove a
formula which equates such open GW invariants with closed GW invariants of
certain $X$-bundles over $\mathbb{P}^1$ used to construct the Seidel
representations for $X$. We apply this formula and degeneration techniques to
explicitly calculate all these open GW invariants. This yields a formula for
the disc potential of $X$, an enumerative meaning of mirror maps, and a
description of the inverse of the ring isomorphism of Fukaya-Oh-Ohta-Ono.
