We demonstrate how solutions to the incompressible Navier-Stokes Equations with transport and advection noise can be recovered through recent developments in the solution theory for stochastic partial differential equations (SPDEs). Local-in-time and global-in-time results are presented. Applications to the Stochastic Navier-Stokes Equations posed on the torus and a smooth bounded domain are detailed; in the latter case, both the no-slip and Navier boundary conditions are considered. Martingale weak solutions in 3D and weak solutions in 2D are proven in all cases. In 2D, strong solutions for the torus and Navier boundary are shown, whilst local strong solutions on the torus in 3D are also retrieved.