  We prove that the inverse of a mirror map for a toric Calabi-Yau manifold of
the form $K_Y$, where $Y$ is a compact toric Fano manifold, can be expressed in
terms of generating functions of genus 0 open Gromov-Witten invariants defined
by Fukaya-Oh-Ohta-Ono \cite{FOOO10}. Such a relation between mirror maps and
disk counting invariants was first conjectured by Gross and Siebert
\cite[Conjecture 0.2 and Remark 5.1]{GS11} as part of their program, and was
later formulated in terms of Fukaya-Oh-Ohta-Ono's invariants in the toric
Calabi-Yau case in \cite[Conjecture 1.1]{CLL12}.
