During the laser powder bed fusion (L-PBF) process, the built part undergoes multiple rapid heating-cooling cycles, leading to complex microstructures with nonuniform properties. In the present work, a computational framework, which weakly couples a finite element thermal model to a non-equilibrium PF model was developed to investigate the rapid solidification microstructure of a Ni-Nb alloy during L-PBF. The framework is utilized to predict the spatial variation of the morphology and size of cellular segregation structure as well as the microsegregation in single-track melt pool microstructures obtained under different process conditions. A solidification map demonstrating the variation of microstructural features as a function of the temperature gradient and growth rate is presented. A planar to cellular transition is predicted in the majority of keyhole mode melt pools, while a planar interface is predominant in conduction mode melt pools. The predicted morphology and size of the cellular segregation structure agrees well with experimental measurements.