A theory of current noise in photoronducting devices, developed on the basis of a large set of measurements concerning the behavior of photoconductivity, photoresponsivity, and noise as a function of light intensity and wavelength in CdS-based photoconductors, is presented. The theory is based on a barrier-type photoconduction model and embodies, in a single general expression of the noise power spectrum, the contributions due to the generation recombination and to the flicker noise (intrinsic noise) as well as to the noise generated by the fluctuation of the potential barrier that controls the electron injection from the metal electrode into the conduction band of the photoconducting material (photoinduced noise). According to the model, the height of this barrier depends on a balance effect between the light-induced positive static charge (ionized deep donor centers or trapped holes) and the negative space charge due to the injected electrons. The fluctuation of the number of ionized centers or trapped holes causes a fluctuation of the potential barrier and thus of the conductance of the device. The transport process is described as a stream of conduction electrons crossing the fluctuating potential barrier and undergoing thermally activated trapping-detrapping processes within the photoconductor bulk. General expressions for the behavior of the photoconductance vs light intensity and for the photoconductance fluctuation power spectrum are worked out on the basis of this model and checked in the following paper by comparison with the experimental results. As shown there, the theory accounts for the shape and the relative changes of the noise power spectra, when the light intensity and the wavelength are varied, without any free parameter. The absolute value of the noise power density is also well reproduced without free parameters in the low-frequency range, where the photoinduced noise dominates. At higher frequencies, where the intrinsic noise becomes important, the noise power spectrum is also nicely fitted with very reasonable values of those quantities that have not been directly measured on the device. The same values of the quantities giving the correct photoconductance fluctuation spectra also reproduce the photoconductance vs light intensity curve calculated according to the proposed barrier photoconductance model.