The exact average bit error probability (BEP) of decode-and-forward (DF) cooperative systems with relay selection for binary phase-shift keying (BPSK) signals in Nakagami- $m$ fading channels is derived. Two types of relay selection schemes, i.e., signal-to-noise ratio (SNR)-based relay selection and log-likelihood-ratio-based relay selection, are investigated, assuming that there are no feedback channels from the destination to the relays. Two types of receivers, i.e., a $\lambda$-maximal ratio combining receiver and a piecewise linear receiver, are examined. The BEP analysis for DF cooperative systems employing BPSK signals is used to derive symbol error probability upper bounds of DF cooperative systems with SNR-based relay selection for quadrature phase-shift keying and 16-quadrature amplitude modulation (16-QAM) signals.