This paper analyzes the ergodic capacity of the MIMO multi-keyhole channel, assuming that the channel state information (CSI) is available only at the receiver. We first derive new closed-form expressions for marginal probability density function (pdf) of the single unordered eigenvalue as well as joint pdf of ordered eigenvalues of the channel matrix in a simple and general framework. With these statistical results, we then present an exact closed-form expression for the ergodic capacity. We analyze tight bounds on the exact capacity and propose a new tight lower bound. We also investigate the asymptotic capacity performances in low-signal-to-noise-ratio (SNR) and high-SNR regimes to gain further insights. All our results apply for arbitrary number of keyholes and antennas. Numerical simulations are presented to validate our theoretical analysis.