This article presents an exact inverse method that generates the airfoil shape, satisfying all fluid dynamic and geometric constraints imposed by prescribing any input velocity distribution (or contour at the hodograph), with the only restriction that it does not take the same vector velocity at two different points of the boundary. The method is supported with a successive conformal mapping technique that can also be used in other problems as the one of grid-generation. The method may be a valuable general tool to obtain optimized designs with excellent performance. It can be extended to generate high-lift airfoils for compressible subsonic flow velocities.