Atomic-level manufacturing is fundamentally concerned with the precise removal, addition, and migration of material at the atomic and close-to-atomic scale (ACS). Tip-based electrochemical deposition, a quintessential ACS electrochemical additive manufacturing technique, offers promising prospects for achieving bottom-up fabrication of metallic micro/nano structures. However, the complex physicochemical reactions involved in electrodes lead to a limited understanding of the mechanisms underlying atomic electrodeposition and structural evolution. For the first time, this study proposes electric double-layer controlled electrochemical kinetics and investigates the effect of direct current (DC) and pulse current (PC) on nickel atomic electrodeposition using molecular dynamics (MD) simulations. The findings reveal that compared to DC electrodeposition, PC electrodeposition results in more orderly deposition morphology, improved surface smoothness, reduced dislocation density, and lower crystal distortion, with these effects being particularly pronounced under low pulse duty ratio conditions. In addition, the pulse frequency significantly influences the morphology and structure of the deposit. The high pulse frequency yields smoother surfaces with local protrusions, while the low frequency favors the formation of orderly and dense structures excepting slightly increased roughness. This study provides critical insights into understanding the microscopic mechanisms of atomic-scale electrodeposition processes and achieving atomically controlled tip-based electrochemical additive manufacturing of micro/nanodevices.