One of the prominent reasons behind the deterioration of cardiovascular conditions is hypertension. Due to lack of specific symptoms, sometimes existing hypertension goes unnoticed until significant damage happens to the heart or any other body organ. Monitoring of BP at a higher frequency is necessary so that we can take early preventive measures to control and keep it within the normal range. The cuff-based method of measuring BP is inconvenient for frequent daily measurements. The cuffless BP measurement method proposed in this paper uses features extracted from the electrocardiogram (ECG) and photoplethysmography (PPG). ECG and PPG both have distinct characteristics, which change with the change of blood pressure levels. Feature extraction and hybrid feature selection algorithms are followed by a generalized penalty-based regression technique led to a new BP measurement process that uses the minimum number of features. The performance of the proposed technique to measure blood pressure was compared to an approach using an ordinary linear regression method with no feature selection and to other contemporary techniques. MIMIC-II database was used to train and test our proposed method. The root mean square error (RMSE) for systolic blood pressure (SBP) improved from 11.2 mmHg to 5.6 mmHg when the proposed technique was implemented and for diastolic blood pressure (DBP) improved from 12.7 mmHg to 6.69 mmHg. The mean absolute error (MAE) was found to be 4.91 mmHg for SBP and 5.77 mmHg for DBP, which have shown improvement over other existing cuffless techniques where the substantial number of patients, as well as feature selection algorithm, were implemented. In addition, according to the British Hypertension Society standard (BHS) standard for cuff-based BP measurement, the criteria for acceptable measurement are to achieve at least grade B; our proposed method also satisfies this criterion.