  In this article we provide a stack-theoretic framework to study the universal
tropical Jacobian over the moduli space of tropical curves. We develop two
approaches to the process of tropicalization of the universal compactified
Jacobian over the moduli space of curves -- one from a logarithmic and the
other from a non-Archimedean analytic point of view. The central result from
both points of view is that the tropicalization of the universal compactified
Jacobian is the universal tropical Jacobian and that the tropicalization maps
in each of the two contexts are compatible with the tautological morphisms. In
a sequel we will use the techniques developed here to provide explicit
polyhedral models for the logarithmic Picard variety.
