In this article, the problem of distributed finite-time consensus control for a class of stochastic nonlinear multiagent systems (MASs) (with directed graph communication) in the presence of unknown dynamics of agents, stochastic perturbations, external disturbances (mismatched and matched), and input saturation nonlinearities is addressed and studied. By combining the backstepping control method, the command filter technique, a finite-time auxiliary system, and artificial neural networks, innovative control inputs are designed and proposed such that outputs of follower agents converge to the output of the leader agent within a finite time. Radial-basis function neural networks (RBFNNs) are employed to approximate unknown dynamics, stochastic perturbations, and external disturbances. To overcome the complexity explosion problem of the conventional backstepping method, a novel finite-time command filter approach is proposed. Then, to deal with the destructive effects of input saturation nonlinearities, the finite-time auxiliary system is designed and developed. By mathematical analysis, it is proven that the mentioned MAS (injected by the proposed control inputs) is semiglobally finite-time stable in probability (SGFSP) and all consensus tracking errors converge to a small neighborhood of the zero during a finite time. Finally, a numerical simulation onto a group of four single-link robot manipulators is carried out to illustrate the effectiveness of the suggested control scheme.