Ultraviolet Nanosecond Laser Annealing (LA) is a powerful tool for both fundamental investigations of ultrafast, nonequilibrium phase-change phenomena and technological applications (e.g., the processing of 3D sequentially integrated nano-electronic devices) where strongly confined heating and melting is desirable. Optimizing the LA process along with the experimental design is challenging, especially when involving complex 3D-nanostructured systems with various shapes and phases. To this purpose, it is essential to model critical nanoscale physical LA-induced phenomena, such as shape changes or formation and evolution of point and extended defects. To date, LA simulators are based on continuum models, which cannot fully capture the microscopic kinetics of a solid-liquid interface. In this work a fully atomistic LA simulation methodology is presented, based on the parallel coupling of a continuum, finite elements, μm-scale electromagnetic-thermal solver with a super-lattice Kinetic Monte Carlo atomistic model for melting. Benchmarks against phase-field models and experimental data validate the approach. LA of a Si(001) surface is studied varying laser fluence and pulse shape, assuming both homogeneous and inhomogeneous nucleation, revealing how liquid Si nuclei generate, deform and coalesce during irradiation. The proposed methodology is applicable to any system where the atom kinetics is determined by a strongly space-and time-dependent field, such as temperature or strain.