Handwritten signatures are still one of the most used and accepted methods for user authentication. They are used in a wide range of human daily tasks, including applications from banking to legal processes. The signature verification problem consists of verifying whether a given handwritten signature was generated by a particular person, by comparing it (directly or indirectly) to genuine signatures from that person. In this research work, a new offline writer-independent signature verification method is introduced (namedbased on a combination of handcrafted Moving Least-Squares features and features transferred from a convolutional neural network. In our experiments, VerSig-R outperforms state-of-the-art techniques on Western-style signatures (CEDAR dataset), while also obtaining competitive results on South Asian-style handwriting (Bangla and Hindi datasets). Furthermore, a wide range of experiments demonstrate that VerSig-R is the most robust in relation to differences in scale and rotation of the signature images. This work also presents a discussion on dataset bias and on cross-dataset performance of VerSig-R, as well as a small user study showing that the proposed technique outperforms the expected human accuracy on the signature-verification task. Finally, a discussion on the impact of the number of signature examples (per writer) used during training on performance and execution time is presented.