This paper proposes a novel distributed stochastic consensus seeking algorithm for networked nonholonomic wheeled mobile robots (NNWMRs) and its application to consensus-based formation. Time-varying delays and noisy measurement are incorporated into the dynamic model to represent two key issues inherently appearing in the communication and information exchange process among robots. Based on backstepping technique and sliding mode approach, the proposed consensus algorithm integrates kinematic controller and dynamic torque controller into the control protocol. A key feature of the proposed consensus algorithm is the introduction of the consensus gains, which characterizes the effects of time delays and noisy measurement. A unified methodology is provided for the convergence analysis of the networked system by using the generalized stochastic delayed Halanay inequality. It is shown that time delays and noisy measurement can play crucial roles in distributed consensus seeking in collaborative multirobot systems. Illustrative examples and simulations are provided to demonstrate and validate the theoretical results.