This paper proposes a novel joint computation and communication cooperation approach in mobile edge computing (MEC) systems, which enables user cooperation in both computation and communication for improving the MEC performance. In particular, we consider a basic three-node MEC system that consists of a user node, a helper node, and an access point (AP) node attached with an MEC server. We focus on the user's latency-constrained computation over a finite block, and develop a four-slot protocol for implementing the joint computation and communication cooperation. Under this setup, we jointly optimize the computation and communication resource allocation at both the user and the helper, so as to minimize their total energy consumption subject to the user's computation latency constraint. We provide the optimal solution to this problem. Numerical results show that the proposed joint cooperation approach significantly improves the computation capacity and the energy efficiency at the user and helper nodes, as compared to other benchmark schemes without such a joint design.