Energy-harvesting series electromagnetic-tuned mass dampers (EMTMDs) have been recently proposed for dual-functional energy harvesting and robust vibration control by integrating the tuned mass damper (TMD) and electromagnetic shunted resonant damping. In this paper, we derive ready-to-use analytical tuning laws for the energy-harvesting series EMTMD system when the primary structure is subjected to force or ground excitations. Both vibration mitigation and energy-harvesting performances are optimized using H2 criteria to minimize root-mean-square (RMS) values of the deformation of the primary structure or maximize the average harvestable power. These analytical tuning laws can easily guide the design of series EMTMDs under various external excitations. Later, extensive numerical analysis is presented to show the effectiveness of the series EMTMDs. The numerical analysis shows that the series EMTMD more effectively mitigates the vibration of the primary structure nearly across the whole frequency spectrum, compared to that of classic TMDs. Simultaneously, the series EMTMD can better harvest energy due to its broader bandwidth effect. Beyond simulations, this paper also experimentally verifies the effectiveness of the series EMTMDs in both vibration mitigation and energy harvesting.