  For each universal genus-$g$ polarization $\mu$ of degree $d$, we construct a
universal tropical Jacobian $J_{\mu,g}^{trop}$ as a generalized cone complex
over the moduli space of stable pointed genus-$g$ tropical curves. We show
several properties of the space $J_{\mu,g}^{trop}$. In particular, we prove
that the natural compactification of $J_{\mu,g}^{trop}$ is the tropicalization
of the Esteves' compactified universal Jacobian over the moduli space of stable
pointed genus-$g$ curves.
