We propose a user selection algorithm and the supporting feedback scheme, for MIMO Gaussian broadcast channels with arbitrary number of users, transmit beamforming and limited channel state information (CSI) available at the transmitter. The method relies on estimation of the user signal-to-interference-plus-noise ratios (SINR's) at the transmitter, by means of an appropriate finite-rate channel report from the mobiles. The basic principle is that users are added successively only if they are beneficial to the system in terms of increased throughput. Numerical results show improved performance compared to other finite-rate feedback schemes.