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The linear algorithm for two-dimensional least square approximation in the frequency domain (2D-FD-LS) is well-established and has been applied successfully to 2D signal representation and image noise cancellation, but it has some limitations. In this paper, a generalized version of the 2D-FD-LS algorithm is developed to overcome such limitations. The generalized version of the 2D-FD-LS algorithm includes extension to complex-valued data and extension to a more general model structure. In addition, a simple model order selection method is presented. An example for system modeling is given also to demonstrate proof-of-concept of the generalized 2D-FD-LS algorithm and the model order selection method.