Shortcuts to isothermality provide a powerful method to speed up quasistatic thermodynamic processes within finite-time manipulation. We employ the shortcut strategy to design and optimize Brownian heat engines, and we formulate a geometric description of the energetics with the thermodynamic length. We obtain a tight and reachable bound of the output power for shortcut-driven heat engines. The bound is reached by the optimal shortcut protocol to vary the control parameters with a proper constant velocity of the thermodynamic length. With the shortcut strategy, we optimize the control of Brownian heat engines to achieve the maximum power in the general-damped situation. We also derive the efficiency at the maximum power and the maximum power at the given efficiency for shortcut-driven heat engines.