Over-the-air computation (OAC) is a promising technique to achieve fast model aggregation across multiple devices in federated edge learning (FEEL). In addition to the analog schemes, one-bit digital aggregation (OBDA) scheme was proposed to adapt OAC to modern digital wireless systems. However, one-bit quantization in OBDA can result in a serious information loss and slower convergence of FEEL. To overcome this limitation, this paper proposes an unsourced massive access (UMA)-based generalized digital OAC (GD-OAC) scheme. Specifically, at the transmitter, all the devices share the same non-orthogonal UMA codebook for uplink transmission. The local model update of each device is quantized based on the same quantization codebook. Then, each device transmits a sequence selected from the UMA codebook based on the quantized elements of its model update. At the receiver, we propose an approximate message passing-based algorithm for efficient UMA detection and model aggregation. Simulation results show that the proposed GD-OAC scheme significantly accelerates the FEEL convergences compared with the state-of-the-art OBDA scheme while using the same uplink communication resources.