We propose a novel resource efficient analog over-the-air (OTA) computation framework to address the demanding requirements of the uplink (UL) fronthaul between the access points (APs) and the central processing unit (CPU) in cell-free massive multiple-input multiple-output (MIMO) systems. We discuss the drawbacks of the wired and wireless fronthaul solutions, and show that our proposed mechanism is efficient and scalable as the number of APs increases. We present the transmit precoding and two-phase power assignment strategies at the APs to coherently combine the signals OTA in a spectrally efficient manner. We derive the statistics of the APs' locally available signals which enable us to to obtain the analytical expressions for the Bayesian and classical estimators of the OTA combined signals. We empirically evaluate the normalized mean square error (NMSE), symbol error rate (SER), and the coded bit error rate (BER) of our developed solution and benchmark against the state-of-the-art wired fronthaul based system.