Multicell cooperation is a promising technique to mitigate the inter-cell interference and improve the sum rate in cellular systems. Limited feedback design is of great importance to base station cooperation as it provides the quantized channel state information (CSI) of both the desired and interfering channels to the transmitters. Most studies on multicell limited feedback deal with scenarios of a single receive antenna at the mobile user. This paper, however, applies limited feedback to cooperative multicell multiple-input multiple-output (MIMO) systems where both base stations and users are equipped with multiple antennas. An optimized feedback strategy with random vector quantization (RVQ) codebook is proposed for interference aware coordinated beamforming that approximately maximizes the lower bound of the sum rate. By minimizing the upper-bound on the mean sum-rate loss induced by the quantization errors, we present a feedback-bit allocation algorithm to divide the available feedback bits between the desired and interfering channels for arbitrary number of transmit and receive antennas under different interfering signal strengths. Simulation results demonstrate that the proposed scheme utilizes the feedback resource effectively and achieves sum-rate performance reasonably close to the full CSI case.