With files proactively stored at base stations (BSs), mobile edge caching enables direct content delivery without remote file fetching, which can reduce the end-to-end delay while relieving backhaul pressure. To effectively utilize the limited cache size in practice, cooperative caching can be leveraged to exploit caching diversity, by allowing users served by multiple base stations under the emerging user-centric network architecture. This paper explores delay-optimal cooperative edge caching in large-scale user-centric mobile networks, where the content placement and cluster size are optimized based on the stochastic information of network topology, traffic distribution, channel quality, and file popularity. Specifically, a greedy content placement algorithm is proposed based on the optimal bandwidth allocation, which can achieve (1-1/e)-optimality with linear computational complexity. In addition, the optimal user-centric cluster size is studied, and a condition constraining the maximal cluster size is presented in explicit form, which reflects the tradeoff between caching diversity and spectrum efficiency. Extensive simulations are conducted for analysis validation and performance evaluation. Numerical results demonstrate that the proposed greedy content placement algorithm can reduce the average file transmission delay up to 50% compared with the non-cooperative and hit-ratio-maximal schemes. Furthermore, the optimal clustering is also discussed considering the influences of different system parameters.