We present the results of the ground- and space-based optical and near-infrared (NIR) follow-up of 224 galaxy cluster candidates detected with the Sunyaev-Zel'dovich (SZ) effect in the 720deg^2^ of the South Pole Telescope (SPT) survey completed in the 2008 and 2009 observing seasons. We use the optical/NIR data to establish whether each candidate is associated with an overdensity of galaxies and to estimate the cluster redshift. Most photometric redshifts are derived through a combination of three different cluster redshift estimators using red-sequence galaxies, resulting in an accuracy of {Delta}z/(1+z)=0.017, determined through comparison with a subsample of 57 clusters for which we have spectroscopic redshifts. We successfully measure redshifts for 158 systems and present redshift lower limits for the remaining candidates. The redshift distribution of the confirmed clusters extends to z=1.35 with a median of z_med_=0.57. Approximately 18% of the sample with measured redshifts lies at z>0.8. We estimate a lower limit to the purity of this SPT SZ-selected sample by assuming that all unconfirmed clusters are noise fluctuations in the SPT data. We show that the cumulative purity at detection significance {xi}>5 ({xi}>4.5) is >=95% (>=70%). We present the red brightest cluster galaxy (rBCG) positions for the sample and examine the offsets between the SPT candidate position and the rBCG. The radial distribution of offsets is similar to that seen in X-ray-selected cluster samples, providing no evidence that SZ-selected cluster samples include a different fraction of recent mergers from X-ray-selected cluster samples.