The development of steady wake flow downstream of a cylindrical rod within a curved channel under the influence of positive, negative, and zero streamwise pressure gradients is theoretically and experimentally investigated. The measured asymmetric wake quantities, such as the mean velocity, turbulent fluctuations in longitudinal and lateral directions, and the turbulent shear stress, are transformed from the probe coordinate system into the curvilinear wake coordinate system. For the transformed nondimensionalized velocity defect and the turbulent quantities, affine profiles are observed throughout the flow regime. Based on the experimental observations and using the transformed equations of motion and continuity, a theoretical framework that generally describes a two-dimensional curvilinear steady wake flow is developed. The theory treats the straight wake flow as a special case for which the curvature radius approaches infinity. A comparison of the developed theory with our own experimental results and with the re-evaluated experimental data from the literature establishes the general validity of the theory.