Applicability of intravoxel incoherent motion (IVIM) imaging in the clinical setting is hampered by the limited reliability in particular of the perfusion-related parameter estimates. To alleviate this problem, various advanced postprocessing methods have been introduced. However, the underlying algorithms are not readily available and generally suffer from an increased computational burden. Contrary, several computationally fast image denoising methods have recently been proposed which are accessible online and may improve reliability of IVIM parameter estimates. The objective of the present work is to investigate the impact of image denoising on accuracy and precision of IVIM parameter estimates using comprehensive in-silico and in-vivo experiments. Image denoising is performed with four different algorithms that work on magnitude data: two algorithms which are based on nonlocal means (NLM) filtering, one algorithm that relies on local principal component analysis (LPCA) of the diffusion-weighted images, and another algorithms that exploits joint rank and edge constraints (JREC). Accuracy and precision of IVIM parameter estimates is investigated in an in-silico brain phantom and an in-vivo ground truth as a function of the signal-to-noise ratio for spatially homogenous and inhomogenous levels of Rician noise. Moreover, precision is evaluated using bootstrap analysis of in-vivo measurements. In the experiments, IVIM parameters are computed a) by using a segmented fit method and b) by performing a biexponential fit of the entire attenuation curve based on nonlinear least squares estimates. Irrespective of the fit method, the results demonstrate that reliability of IVIM parameter estimates is substantially improved by image denoising. The experiments show that the LPCA and the JREC algorithms perform in a similar manner and outperform the NLM-related methods. Relative to noisy data, accuracy of the IVIM parameters in the in-silico phantom improves after image denoising by 76-79%, 79-81%, 84-99% and precision by 74-80%, 80-83%, 84-95% for the perfusion fraction, the diffusion coefficient, and the pseudodiffusion coefficient, respectively, when the segmented fit method is used. Beyond that, the simulations reveal that denoising performance is not impeded by spatially inhomogeneous levels of Rician noise in the image. Since all investigated algorithms are freely available and work on magnitude data they can be readily applied in the clinical setting which may foster transition of IVIM imaging into clinical practice.