Image denoising is a central problem in image processing and it is often a necessary step prior to higher level analysis such as segmentation, reconstruction or super-resolution. The non-local means (NL-means) perform denoising by exploiting the natural redundancy of patterns inside an image; they perform a weighted average of pixels whose neighborhoods (patches) are close to each other. This allows to reduce significantly the noise while preserving most of the image content. While it performs well on flat areas and textures, it might leave a residual noise around edges and singular structures. We introduce in this paper a variational approach that reduces this residual noise by adaptively regularizing non-local methods with the total variation. The classical minimization of the total variation - the ROF model - leads to restore regular images but it is prone to over-smooth textures and create a staircasing effect on flat areas. The proposed regularized NL-means algorithm combines these methods and reduce both of their respective defaults by minimizing the total variation with a non-local data fidelity term. Besides, this model adapts to different noise statistics and a fast solution can be obtained in the general case of the exponential family. We develop this model for image denoising and then we adapt it to video denoising, where it enables us to use 3D patches.