In this paper, we propose a novel automated double auction mechanism called convergent linear function submission-based double-auction (CLFS-DA) for a prosumers’ decentralized smart grid. The target decentralized smart grid is a regional electricity network that consists of many prosumers that have a battery and a renewable energy-based generator, such as photovoltaic cells. In the proposed double-auction mechanism, each intelligent software agent representing each prosumer submits linear demand and supply functions to an automated regional electricity market where they are registered. It is proven that the CLFS-DA mechanism is guaranteed to obtain one of the global optimal price profiles in addition to it achieving an exact balance between demand and supply, even through the learning period. The proof of convergence is provided on the basis of the theory of LFS-DA, which gives a clear bridge between a function submission-based double auction and a dual decomposition (DD)-based real-time pricing procedure. The performance of the proposed mechanism is demonstrated numerically through a simulation experiment.