Driven by the urgent requirement of ubiquitous and reliable coverage for global users, the low earth orbit (LEO) satellite network has attracted numerous attentions from the academic and industry circles. By deploying multi-access edge computing (MEC) servers in LEO satellites, computation offloading and content caching services can be provided for remote Internet-of-Things (IoT) devices without proximal servers. In this paper, the joint optimization of computation offloading, radio resource allocation and caching placement in LEO satellite MEC networks are investigated. The problem is formulated to minimize the total delay of all ground IoT devices while ensuring the energy, computing and caching constraints. To solve this mixed-integer and non-convex problem, a Lagrange dual decomposition (LDD)-based algorithm is proposed to obtain the closed-form optimal solution. Then, a heuristic algorithm is proposed to further reduce the computation complexity. Numerical results validate that both algorithms are effective compared to the optimal exhaustive search, the full local computing and the full MEC methods. Besides, the offloading ratio and the average delay of all IoT devices with different numbers and computing capacities of devices and satellites are also demonstrated.INDEX TERMS LEO satellites, multi-access edge computing, computation offloading, resource allocation, caching.