In this paper, multiple-input multiple-output systems employing space-time block codes (STBCs) with transmit antenna selection (TAS) are examined for flat Nakagami-m fading channels. Exact symbol error rate (SER) expressions for M-ary modulation techniques are derived by using the moment generating function based analysis method. In the SER analysis, the receiver is assumed to use maximal ratio combining whereas a subset of transmit antennas that maximizes the instantaneous received signal-to-noise ratio (SNR) is selected for STBC transmission. The analytical SER results are validated by Monte Carlo simulations. By deriving upper and lower bounds for SER expressions, it is shown that TAS/STBC schemes achieve full diversity orders at high SNRs.