A component based method (CompCor) for the reduction of noise in both blood oxygenation level-dependent (BOLD) and perfusion-based functional magnetic resonance imaging (fMRI) data is presented. In the proposed method, significant principal components are derived from noise regions-of-interest (ROI) in which the time series data are unlikely to be modulated by neural activity. These components are then included as nuisance parameters within general linear models for BOLD and perfusion-based fMRI time series data. Two approaches for the determination of the noise ROI are considered. The first method uses high-resolution anatomical data to define a region of interest composed primarily of white matter and cerebrospinal fluid, while the second method defines a region based upon the temporal standard deviation of the time series data. With the application of CompCor, the temporal standard deviation of resting-state perfusion and BOLD data in gray matter regions was significantly reduced as compared to either no correction or the application of a previously described retrospective image based correction scheme (RETROICOR). For both functional perfusion and BOLD data, the application of CompCor significantly increased the number of activated voxels as compared to no correction. In addition, for functional BOLD data, there were significantly more activated voxels detected with CompCor as compared to RETROICOR. In comparison to RETROICOR, CompCor has the advantage of not requiring external monitoring of physiological fluctuations.