Cardiovascular diseases (CVDs) affect components of the circulatory system responsible for transporting blood through blood vessels. The measurement of the mechanical force acting on the walls of blood vessels, as well as the blood flow between heartbeats and when the heart is at rest, is known as blood pressure (BP). Regular assessment of BP can aid in the prevention and early detection of CVDs. In the present research, a deep learning algorithm was developed to accurately calculate both blood pressure (BP) and heart rate (HR) by extracting relevant features from photoplethysmogram (PPG), electrocardiogram (ECG), and ABP signals. This algorithm was implemented using the Medical Information Mart for Intensive Care (MIMIC-II) dataset. It captures vital blood pressure-related features extracted from the PPG signal and accounts for the time relationship with the ECG. The algorithm also determines the values of systolic blood pressure (SBP) and diastolic blood pressure (DBP) based on the ABP waveform through a convolutional neural network and stepwise multivariate linear regression. In comparison with other established BP measurement methods, our proposed approach achieved better results, with a mean absolute error (MAE) of approximately 4.7 mmHg for SBP and 2.1 mmHg for DBP, respectively. The standard deviation (STD) for SBP and DBP was approximately 7.6 mmHg and 3.9 mmHg, respectively. This study makes a valuable contribution to the healthcare field by introducing a novel, cost-effective continuous BP measurement method with improved accuracy while also minimizing the data dimension without losing any important information.