Continuous vital signal monitoring is becoming more relevant in preventing diseases that afflict a large part of the world’s population; for this reason, healthcare equipment should be easy to wear and simple to use. Non-intrusive and non-invasive detection methods are a basic requirement for wearable medical devices, especially when these are used in sports applications or by the elderly for self-monitoring. Arterial blood pressure (ABP) is an essential physiological parameter for health monitoring. Most blood pressure measurement devices determine the systolic and diastolic arterial blood pressure through the inflation and the deflation of a cuff. This technique is uncomfortable for the user and may result in anxiety, and consequently affect the blood pressure and its measurement. The purpose of this paper is the continuous measurement of the ABP through a cuffless, non-intrusive approach. The approach of this paper is based on deep learning techniques where several neural networks are used to infer ABP, starting from photoplethysmogram (PPG) and electrocardiogram (ECG) signals. The ABP was predicted first by utilizing only PPG and then by using both PPG and ECG. Convolutional neural networks (ResNet and WaveNet) and recurrent neural networks (LSTM) were compared and analyzed for the regression task. Results show that the use of the ECG has resulted in improved performance for every proposed configuration. The best performing configuration was obtained with a ResNet followed by three LSTM layers: this led to a mean absolute error (MAE) of 4.118 mmHg on and 2.228 mmHg on systolic and diastolic blood pressures, respectively. The results comply with the American National Standards of the Association for the Advancement of Medical Instrumentation. ECG, PPG, and ABP measurements were extracted from the MIMIC database, which contains clinical signal data reflecting real measurements. The results were validated on a custom dataset created at Neuronica Lab, Politecnico di Torino.