We present a method for training neural networks with synthetic electrocardiograms that mimic signals produced by a wearable single lead electrocardiogram monitor. We use domain randomization where the synthetic signal properties such as the waveform shape, RR-intervals and noise are varied for every training example. Models trained with synthetic data are compared to their counterparts trained with real data. Detection of r-waves in electrocardiograms recorded during different physical activities and in atrial fibrillation is used to assess the performance. By allowing the randomization of the synthetic signals to increase beyond what is typically observed in the real-world data the performance is on par or superseding the performance of networks trained with real data. Experiments show robust model performance using different seeds and on different unseen test sets that were fully separated from the training phase. The ability of the model to generalize well to hidden test sets without any specific tuning provides a simple and explainable alternative to more complex adversarial domain adaptation methods for model generalization. This method opens up the possibility of extending the use of synthetic data towards domain insensitive cardiac disease classification when disease specific a priori information is used in the electrocardiogram generation. Additionally, the method provides training with free-to-collect data with accurate labels, control of the data distribution eliminating class imbalances that are typically observed in health-related data, and the generated data is inherently private.