An analytically exact method is proposed to extract the signal intensity and the noise variance simultaneously from noisy magnitude MR signals. This method relies on a fixed point formula of signal-to-noise ratio (SNR) and a correction factor. The correction factor, which is a function of SNR, establishes a fundamental link between the variance of the magnitude MR signal and the variance of the underlying Gaussian noise in the two quadrature channels. A more general but very similar method is developed for parallel signal acquisitions with multiple receiver coils. In the context of MR imaging, the proposed method can be carried out on a pixel-by-pixel basis if the mean and the standard deviation of the magnitude signal are available.