An interferometric signal processing method for localizing a broadband moving sound source in an oceanic waveguide is proposed and studied theoretically and experimentally. The field of a moving sound source in waveguide creates a stable interference pattern of the intensity distribution (interferogram) I(ω,t) in the frequency-time domain. Sound intensity is accumulated along interference fringes over the observation time. The two-dimensional Fourier transform (2D-FT) is applied to analyze the interferogram I(ω,t). The result of the 2D-FT F(τ,ν) is called the Fourier-hologram (hologram). The mathematical theory of hologram structure F(τ,ν) is developed in the present paper. It is shown that the hologram F(τ,ν) allows the coherent accumulation of sound intensity of the interferogram in a relatively small area focal spots. The presence of these focal spots is the result of interference of acoustic modes with different wave numbers. The main result of this paper is a simple relationship between the focal spots coordinates on the hologram and the source range, velocity, and motion direction. The proposed interferometric signals processing method for source localization is validated using experimental observations and numerical modeling in the band 80-120 Hz. The estimations of source range, velocity, and motion direction are performed for different cases of source motion.