Proactive wireless caching and device to device (D2D) communication have emerged as promising techniques for enhancing users' quality of service and network performance. In this paper, we propose a new architecture for D2D caching with inter-cluster cooperation. We study a cellular network in which users cache popular files and share them with other users either in their proximity via D2D communication or with remote users using cellular transmission. We characterize the network average delay per request from a queuing perspective. Specifically, we formulate the delay minimization problem and show that it is NP-hard. Furthermore, we prove that the delay minimization problem is equivalent to the minimization of a non-increasing monotone supermodular function subject to a uniform partition matroid constraint. A computationally efficient greedy algorithm is proposed which is proven to be locally optimal within a factor (1- e ^-1 ) ≈ 0.63 of the optimum. We analyze the average per request throughput for different caching schemes and conduct the scaling analysis for the average sum throughput. We show how throughput scaling depends on video content popularity when the number of files grows asymptotically large. Simulation results show a delay reduction of 45% to 80% compared to a D2D caching system without inter-cluster cooperation.