Analysis of mutational signatures is a powerful approach for understanding the mutagenic processes that have shaped the evolution of a cancer genome. Here we present SigProfilerAssignment, a desktop and an online computational framework for assigning all types of mutational signatures to individual samples. SigProfilerAssignment is the first tool that allows both analysis of copy-number signatures and probabilistic assignment of signatures to individual somatic mutations. As its computational engine, the tool uses a custom implementation of the forward stagewise algorithm for sparse regression and nonnegative least squares for numerical optimization. Analysis of 2,700 synthetic cancer genomes with and without noise demonstrates that SigProfilerAssignment outperforms four commonly used approaches for assigning mutational signatures. SigProfilerAssignment is freely available at https://github.com/AlexandrovLab/SigProfilerAssignment with a web implementation at https://cancer.sanger.ac.uk/signatures/assignment/.