This article addresses the optimal (minimum-input-energy) output-transition problem for linear systems. The goal is to transfer the output from an initial value y(t) = (y) under bar (for all time t less than or equal to t(i)) to a final output value y(t) = (y) over bar (for all time t greater than or equal to t(f)). Previous methods solve this output-transition problem by transforming it into a state-transition problem; the initial and final states (x(t(i)),x(t(f)), respectively) are chosen and a minimum-energy state-to-state transition problem is solved. However, the choice of the initial and final states can be ad hoc and the resulting output-transition cost (input energy) may not be minimal. The contribution of this article is the solution of the optimal output-transition problem. An example system with elastic dynamics is studied to illustrate the proposed method. Simulation results are presented that show substantial reduction of transition costs with the use of the proposed method when compared to the use of minimum-energy state-to-state transitions.