Automatic modulation classification (AMC) is a key component of intelligent communication systems used in various military and cognitive radio applications. In AMC, it is desired to increase the number of different modulation formats that can be classified, reduce the computational complexity of classification, and improve the robustness and accuracy of the classifier. Generally, AMC techniques are classified into feature based (FB) and likelihood based (LB) classifiers. In this paper, we propose a novel hierarchical hybrid automatic modulation classifier (HH-AMC) that employs both feature based and likelihood based classifiers to improve performance and reduce complexity. As another major contribution of this paper, we implement and evaluate the performance of HH-AMC over-the-air (OTA) using software defined radios (SDRs) to demonstrate the feasibility of the proposed scheme in practice. Experimental evaluation shows high probability of correct classification (Pcc) for both linear and non-linear modulation formats including BPSK, QPSK, 8-PSK, 16-QAM, 32-QAM, CPFSK, GFSK and GMSK under lab conditions.