Precise and reliable apodization of silicon integrated Bragg gratings (IBGs) is the key to realizing their spectral tailoring for many optical applications such as optical signal processing and wavelength-division multiplexing systems. However, apodization in a silicon IBG that is typically realized by modifying the physical waveguide grating structure can also introduce unwanted grating phase variations that can affect the grating response. In this paper, we present a model to characterize apodized silicon IBGs which can take such apodization phase noise (APN) into account, based on direct synthesis of the physical grating structure. The model is used to characterize a set of different silicon IBGs apodized by lateral misalignment (ΔL) and duty-cycle (DC) modulations and designed with different responses, and the results show that the APN can greatly distort the complex responses of the gratings. Then, we develop a methodology to compensate the APN and thus to correct the distorted grating responses. The designed silicon IBGs were fabricated and tested experimentally. The accuracy of the model is examined by comparing the measured grating spectra with those predicted by the model. Spectral corrections are then demonstrated in Gaussian-apodized gratings based on ΔL- and DC-modulated silicon IBGs and a square-shaped filter developed on a ΔL-modulated IBG. Finally, a complex spectral correction of a photonic Hilbert transformer developed on a ΔL-modulated silicon IBG is achieved.