Blood pressure (BP) is one of the most important and meaningful vital signs of the human body that can be assessed as a critical risk factor for severe health conditions, especially cardiovascular diseases (CVD) and hypertension. An accurate, continuous and cuff-less BP monitoring technique could help clinicians to improve the rate of prevention, detection, and diagnosis of hypertension and manage related treatment plans. BP is influenced by many factors such as various abnormalities in cardiac output, blood vessel wall elasticity, circulation blood volume, peripheral resistance, respiration, and emotional behaviour. Importantly, the complex and dynamic nature of the cardiovascular system necessitates that any BP monitoring system should benefit from an intelligent technology that can extract and analyze compelling BP features. However, employing handcrafted feature-engineering before estimating the BP is a cumbersome and compute-intensive task. Deep learning techniques could be applied to BP feature extraction and classifying other physiological signals. Moreover, these techniques could be employed for estimating BP as a potential approach for achieving continuous BP measurement. This study aims to develop an optimized convolutional neural network (CNN)-based model to estimate BP using the fundamental capability of CNN algorithms to perform automatic feature extraction, which then precludes the necessity of handcrafted feature engineering. In order to resolve the issue of engineered feature extraction, several techniques are proposed and discussed in this study, which aims to find the best approach to measuring BP. A CNN regression model designed from scratch is proposed to estimate systolic blood pressure (SBP) and diastolic blood pressure (DBP). Scalograms of electrocardiogram (ECG) and photoplethysmography (PPG) signals were created using continuous wavelet transform and were used to train and test the proposed CNN model. The CNN model was also trained and tested with time series of ECG and PPG signals with the intention of finding the best approach to train a CNN network. Furthermore, to enhance and optimize the model design and to estimate the BP value through the relationship between the pulse transit time (PTT) and BP, signal pre-processing and R-peak detection for ECG signals were utilized. The main idea was to ensure that all parameters related to PTT were included in each cardiac sample. The performance of the proposed CNN was compared with an optimized long short-term memory (LSTM)-based model and validated with a pre-processed dataset. A low root mean square error was achieved, which indicated the proposed CNN-based outperformed an LSTM-based model. The study was further extended by proposing a novel hybrid system that combines the CNN model with a support vector regression (SVR) model. The CNN used as a trainable feature extractor, and the SVR performed as the regression operator. Moreover, a set of features were computed and extracted from the same dataset to train the SVR model, and the result was compared to the proposed novel hybrid CNN-SVR. The experimental results demonstrated that the proposed hybrid CNN-SVR model could effectively extract features from ECG and PPG signals and their corresponding SBP and DBP, while achieving higher accuracy and less errors. The hybrid CNN-SVR framework, with its less-complex solution, was selected as an ideal framework for measuring BP among other proposed methods and related studies discussed in the literature. Results of this study showed that the estimated SBP and DBP from the hybrid CNN-SVR framework were highly correlated with the actual SBP and DBP. The proposed model is the first hybrid CNN-SVR BP model for predicting BP to be found in the known literature and offers a significant contribution towards the management of BP and effectiveness of CVD treatments.