Electrocardiogram (ECG) signals consist of data containing measurements of electrical activity in the heartbeats. These signals include relevant information used to detect abnormalities such as arrhythmia. In this study, a recognition system is proposed for detection and classification of heartbeats in ECG signals. Heartbeats in the ECG data were detected by using the wavelet transform (WT) method and these beats are segmented with determined periods. For obtaining distinctive features from the beats, multi-resolution WT is applied to these segmented signals, and wavelet coefficients are obtained from different frequency levels. Feature vectors are generated on these coefficients by using various statistical methods. The proposed recognition system is trained on feature vectors by using the Online Sequential Extreme Learning Machine (OSELM) classifier during the learning phase to automatically recognize the signals. Five different beat types were obtained from the MIT-BIH arrhythmia dataset. The multi-class dataset that includes five classes and the binary-class dataset that includes two classes were created among these beat types. Performance tests of the proposed wavelet-based-OSELM (W-OSELM) method were realized with these two datasets. The proposed recognition system provided 97.29% correct beat detection rate from raw ECG signals. The classification accuracy is 99.44% for the binary-class dataset and 98.51% for the multi-class dataset. Furthermore, the proposed classifier has shown very fast recognition performance on ECG signals.