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A wide range of multi-agent coordination problems including reference tracking and disturbance rejection requirements can be formulated as a cooperative output regulation problem. The general framework captures typical problems such as output synchronization, leader-follower synchronization, and many more. In the present paper, we propose a novel distributed regulator for groups of identical and non-identical linear agents. We consider global external signals affecting all agents and local external signals affecting only individual agents in the group. Both signal types may contain references and disturbances. Our main contribution is a novel coupling among the agents based on their transient state components or estimates thereof in the output feedback case. This coupling achieves transient synchronization in order to improve the cooperative behavior of the group in transient phases and guarantee a desired decay rate of the synchronization error. This leads to a cooperative reaction of the group on local disturbances acting on individual agents. The effectiveness of the proposed distributed regulator is illustrated by a vehicle platooning example and a coordination example for a group of four non-identical 3-DoF helicopter models.