Despite the widespread availability of process modeling tools, the first version of a process model is often drawn by hand on a piece of paper or whiteboard, especially when several people are involved in its elicitation. Though this has been found to be beneficial for the modeling task itself, it also creates the need to manually convert hand-drawn models afterward, such that they can be further used in a modeling tool. This manual transformation is associated with considerable time and effort and, furthermore, creates undesirable friction in the modeling workflow. In this paper, we alleviate this problem by presenting a technique that can automatically recognize and convert a sketch process model into a digital BPMN model. A key driver and contribution of our work is the creation of a publicly available dataset consisting of 502 manually annotated, hand-drawn BPMN models, covering 25 different BPMN elements. Based on this data set, we have established a neural network-based recognition technique that can reliably recognize and transform hand-drawn BPMN models. Our evaluation shows that our technique considerably outperforms available baselines and, therefore, provides a valuable basis to smoothen the modeling process.