We prove that some time discretization schemes for the 2D Navier-Stokes equations on the torus subject to a random perturbation converge in L 2 (Ω). This refines previous results which only established the convergence in probability of these numerical approximations. Using exponential moment estimates of the solution of the stochastic Navier-Stokes equations and convergence of a localized scheme, we can prove strong convergence of fully implicit and semi-implicit time Euler discretizations, and of a splitting scheme. The speed of the L 2 (Ω)-convergence depends on the diffusion coefficient and on the viscosity parameter.2000 Mathematics Subject Classification. Primary 60H15, 60H35; Secondary 76D06, 76M35.