In this paper a deterministic procedure is presented for the synthesis of phase-only reconfigurable aperiodic arrays. The proposed approach develops in three steps: at first, one aperiodic array for each of the desired patterns is derived, then a unique aperiodic geometry is suitably selected, and finally a deterministic phase-only synthesis algorithm is applied to the latter aperiodic array, in order to determine suitable excitation phases and to achieve reconfigurability. Although the optimality of the solution is not guaranteed, a numerical example is proposed to test the method.