This paper develops a cooperative control scheme for a team of distributed agents. Each agent is assumed to evolve in discrete-time and exchange delayed state information with a subset of neighboring or cooperating agents. Delays can be different for each pair of cooperating agents. The control design is derived using a finite-horizon cost function that includes both the regulation and cooperation objectives. The cooperative control problem is formulated in a receding-horizon framework, where the control law can be explicitly broken up in two components: one due feedback from the local state variables and the other based on delayed information gathered from cooperating neighboring agents. Novel theoretical and constructive results are presented, concerning the choice of the cost function in order to guarantee stability of the overall team of agents, and extending sufficient conditions previously established by the authors. Simulation results are used to illustrate the effectiveness of the proposed control scheme.