Arterial blood pressure (ABP) is one of the most vital signs in the prophylaxis and treatment of blood pressure-related diseases because raised blood pressure is the most significant cause of death and the second major cause of disability in the world. Higher ABP yields greater strain on arteries and these extra strains turn arteries into thicker, less flexible, and more narrow structures. This increases the possibility of having an artery busting or artery occlusion, which are the primary reasons for heart attacks, kidney disease, or strokes. In addition to its importance in monitoring cardiovascular homeostasis, measurement of ABP is imperative in surgical operations. In this study, a simple and effective approach was proposed to estimate ABP from electrocardiogram (ECG) and photoplethysmograph (PPG) signals by an extreme learning machine (ELM) and statistical properties of the ECG and/or PPG signals in the time-frequency domain. To evaluate and apply the proposed approach, the Cuffless Blood Pressure Estimation Dataset, which was published and shared by UCI, was employed. First, the statistical properties were extracted from ECG and PPG signals that were in the time-frequency domain. Later, extracted features were employed to estimate cuffless ABP for each subject by the ELM and some popular machine learning methods. Achieved results and reported results in the literature showed that the proposed approach can be successfully employed for estimating cuffless blood pressure (BP) from ECGs and/or PPGs. Additionally, with the proposed approach, the systolic BP, mean BP, and diastolic BP can be calculated simultaneously.