Keyhole mode wobble laser welding is gaining increasing acceptance due to its ability to bridge gaps, refine microstructure, and enhance the mechanical properties of welds. However, the impact of amplitude, frequency, welding speed, laser beam power, and beam radius on the heat flux distribution, melting pattern, and three-dimensional temperature field is not well understood. To address this need, here we report a combined experimental and computational study to investigate the effects of the key wobble welding parameters on the energy distribution impinging on the welding track, keyhole formation, three-dimensional fluid flow and heat transfer during wobble laser welding of Inconel 740H. The modeling results were rigorously tested using experiments in which the welding speed, laser power, and wobble amplitude and frequency were varied. A bimodal power density distribution with higher power density near the edge than in the middle of the track occurred when the wobble amplitude significantly exceeded the laser beam diameter. A high wobble amplitude resulted in a wide and shallow pool while the wobble frequency used in this work did not significantly impact the fusion zone geometry. A set of process maps were constructed to understand the role of wobble laser parameters in achieving a desirable fusion zone geometry during keyhole mode wobble laser welding. Finally, wobble laser welding with a high amplitude was found to favor rapid solidification and the formation of finer solidification microstructure.