<p>In this paper, we design a distributed stochastic source seeking algorithm based on time-delay measurements to implement source seeking and formation control, so that vehicles can achieve and maintain a specific formation during the source seeking process. First, we present continuous-time stochastic averaging theorems for nonlinear delay-differential systems with stochastic perturbations. Then, based on the stochastic extremum seeking method and the leaderless formation strategy, we design a distributed stochastic source seeking algorithm based on time-delay measurements to navigate multiple velocity-actuated vehicles to search for an unknown source while achieving and maintaining a predefined formation, and the effect of the delay is eliminated by adopting the one-stage sequential predictor approach. Moreover, based on our developed stochastic averaging theorems, we prove that the average position of vehicles exponentially converges to a small neighborhood of the source in the almost sure sense, and vehicles can achieve and maintain a predefined formation. Finally, we provide numerical examples to verify the effectiveness of our proposed algorithm.</p>