In this paper, we study the mean-square consensus-ability problem of discrete-time linear multiagent systems over directed networks with constant communication delay and packet dropouts. When the packet dropouts in different communication channels are identical, the consensusability problem is transformed into a simultaneous mean-square stabilization problem of systems with constant time delay and packet dropout. When the packet dropouts are nonidentical, we build the dynamics over edges based on the notion of compressed edge Laplacian for directed graphs to separate the packet dropouts from the network topology. Sufficient consensusability conditions are obtained for both cases in terms of the communication delay, the packet dropout rates, the communication network topology, and the agent dynamics.