An electrodeposition technique is described that produces atomically flat epitaxial metal overlayers of quality similar to that obtained by ultrahigh vacuum techniques at elevated temperature. In this approach, a metal of interest such as silver is co-deposited with a reversibly deposited mediator metal. The mediator is periodically deposited and stripped from the surface, and this serves to significantly increase the density of two-dimensional islands of silver atoms, promoting a layer-by-layer thin-film growth mode. In situ scanning tunneling microscopy was used to demonstrate the growth process for the heteroepitaxial system silver/gold (111) with either lead or copper as the mediator.