After the recent long shutdown of the LHC, the ATLAS detector is now ready to record collision data with several upgrades implemented. The most important and challenging upgrades are those of the ATLAS Muon Spectrometer, where the two forward inner muon stations were replaced by the New Small Wheels (NSW) equipped with two new detector technologies; small strip Thin Gap Chambers (sTGC) and Micromegas (MM). Following the enormous effort for the construction, commissioning and installation of the NSW, the muon software required extensive revisions and new implementations, as well as migration to a new multi-thread approach. The new detectors are now fully integrated into the software. The detector response is simulated and has been compared with real data from cosmic ray test benches and test beams. Nominal geometries, misalignments, and deformations, as well as other possible deviations from the nominal operating conditions resulting from validation studies, have been implemented for a realistic study of final performances. The simulation of both sTGC and MM trigger has been implemented, and the performance has been evaluated in different configurations, with and without background, serving as a crucial input for the optimization of the trigger logic. Full muon reconstruction performance studies are performed and all the software tools, including dedicated data format, are now ready for early data-taking detector commissioning and for physics analyses.