We present the analysis of the complete 3 yr data set obtained with the Degree Angular Scale Interferometer (DASI) polarization experiment, operating from the Amundsen-Scott South Pole research station. New data obtained at the end of the 2002 austral winter and throughout the 2003 season were added to the data from which the first detection of polarization of the cosmic microwave background (CMB) radiation was reported. The analysis of the combined data supports, with increased statistical power, all of the conclusions drawn from the initial data set. In particular, the detection of E-mode polarization is increased to the 6.3 sigma confidence level, TE cross-polarization is detected at 2.9 sigma , and B-mode polarization is consistent with zero, with an upper limit well below the level of the detected E-mode polarization. The results are in excellent agreement with the predictions of the cosmological model that has emerged from CMB temperature measurements. The analysis also demonstrates that contamination of the data by known sources of foreground emission is insignificant.