Human health and quality of life are negatively impacted by apnea, an increasingly prevalent sleep disorder. For monitoring and managing sleep apnea’s side effects and consequences, accurate automatic algorithms for detecting sleep apnea are crucial. In this paper, deep transfer learning methods are employed for the detection of OSA events from Electrocardiograph (ECG) and Photoplethysmography (PPG) signals. ResNet34 is a deep learning model based on convolutional neural networks (CNNs). Transfer learning algorithms such as AlexNet, VGG16, VGG19 and ResNet50 are implemented. In order to train the ResNet34 model data augmentation, optimal learning rate finding, and fine-tuning are used. To obtain generalizable models, a training set of data is divided into three sets: a validation set for adjusting hyperparameters and improving generalizability, and a test set for evaluating generalizability on unknown data. Deep transfer learning models have the best accuracy, sensitivity, specificity, precision, and F1 score with 97.86±1.24%, 99.65%, 97.12%, 98.16% and 98.90% respectively. It can assist sleep lab technicians in screening patients for OSA events continuously through PPG and ECG signals.