We study a multi-agent output regulation problem, where not all agents have access to the exosystem's dynamics. We propose a fully distributed controller that solves the problem for linear, heterogeneous, and uncertain agent dynamics as well as time-varying directed networks. The distributed controller consists of two parts: (1) an exosystem generator that locally estimates the exosystem dynamics, and (2) a dynamic compensator that, by locally approaching the internal model of the exosystem, achieves perfect output regulation. Our approach leverages methods from internal model based controller synthesis and multi-agent consensus over time-varying directed networks; the derived result is a generalization of the (centralized) internal model principle to the distributed, networked setting.