In this study, spatial and temporal profiles of an Nd-YAG laser beam pressure pulse are experimentally characterized and fully captured for use in numerical simulations of laser impact welding (LIW). Both axisymmetric, Arbitrary Lagrangian-Eulerian (ALE) and Eulerian dynamic explicit numerical simulations of the collision and deformation of the flyer and target foils are created. The effect of the standoff distance between the foils on impact angle, velocity distribution, springback, the overall shape of the deformed foils, and the weld strength in lap shear tests are investigated. In addition, the jetting phenomenon (separation and ejection of particles at very high velocities due to high-impact collision) and interlocking of the foils along the weld interface are simulated. Simulation results are compared to experiments, which exhibit very similar deformation and impact behaviors. In contrast to previous numerical studies that assume a pre-defined deformed flyer foil shape with uniform initial velocity, the research in this work shows that incorporation of the actual spatial and temporal profiles of the laser beam and modeling of the corresponding pressure pulse based on a laser shock peening approach provides a more realistic prediction of the LIW process mechanism.