Given an undirected graph G = (N, E) of agents N = {1,..., N} connected with edges in E, we study how to compute an optimal decision on which there is consensus among agents and that minimizes the sum of agent-specific private convex composite functions {Φ _i } _i∈N , where Φ _i ≐ ξ _i + f _i belongs to agent-i. Assuming only agents connected by an edge can communicate, we propose a distributed proximal gradient algorithm (DPGA) for consensus optimization over both unweighted and weighted static (undirected) communication networks. In one iteration, each agent-i computes the prox map of ξ _i and gradient of f _i , and this is followed by local communication with neighboring agents. We also study its stochastic gradient variant, SDPGA, which can only access to noisy estimates of ∇f _i at each agent-i. This computational model abstracts a number of applications in distributed sensing, machine learning and statistical inference. We show ergodic convergence in both suboptimality error and consensus violation for the DPGA and SDPGA with rates O(1/t) and O(1/√t), respectively.