At processing geodetic networks, it is necessary to transform the coordinates of points from one system to another. Two methods are most common: shifting and rotation of the coordinate system, or recalculation through a spatial geodetic one. In the first method, simple formulas are used, but for extended objects, the conformality of the coordinate transformation is violated. In the second one, the parameters of the systems are usually unknown, and a complex mathematical apparatus is used for converting coordinates. The complexity increases when the coordinate systems are built on different spheroids or projections. The transformation is proposed to be performed using the analytical function of a complex variable. The universality and simplicity of this method is proved. The errors do not depend on the projection type and the spheroids’ parameters. Coordinate transformations from Gaussian or UTM projections to another conformal projection or local coordinate system are performed using the same formulas.The accuracy is improved if the coefficients in the formulas are calculated using the smallest squares method.