This paper presents a distributed control framework for leader-follower multi-agent systems with general linear dynamics to achieve consensus alongside prescribed transient performance. The multi-agent system is in a leader-follower configuration with only a set of agents selected as leaders and controlled via external inputs. In particular, we propose a distributed control framework comprising a prescribed performance controller for the leaders, while the followers are governed solely by a consensus protocol. When the decay rate of the performance functions is within a sufficient bound, we show that this distributed control law achieves consensus for the entire multi-agent system, with the guarantee that the trajectories of the consensus errors remain bounded by a time-varying prescribed transient performance function. Finally, the proposed results are illustrated through numerical examples.