  We present a catalog of galaxy clusters selected via their Sunyaev-Zel'dovich
(SZ) effect signature from 2500 deg$^2$ of South Pole Telescope (SPT) data.
This work represents the complete sample of clusters detected at high
significance in the 2500-square-degree SPT-SZ survey, which was completed in
2011. A total of 677 (409) cluster candidates are identified above a
signal-to-noise threshold of $\xi$ =4.5 (5.0). Ground- and space-based optical
and near-infrared (NIR) imaging confirms overdensities of similarly colored
galaxies in the direction of 516 (or 76%) of the $\xi$>4.5 candidates and 387
(or 95%) of the $\xi$>5 candidates; the measured purity is consistent with
expectations from simulations. Of these confirmed clusters, 415 were first
identified in SPT data, including 251 new discoveries reported in this work. We
estimate photometric redshifts for all candidates with identified optical
and/or NIR counterparts; we additionally report redshifts derived from
spectroscopic observations for 141 of these systems. The mass threshold of the
catalog is roughly independent of redshift above $z$~0.25 leading to a sample
of massive clusters that extends to high redshift. The median mass of the
sample is $M_{\scriptsize 500c}(\rho_\mathrm{crit})$ ~ 3.5 x 10$^{14} M_\odot
h^{-1}$, the median redshift is $z_{med}$ =0.55, and the highest-redshift
systems are at $z$>1.4. The combination of large redshift extent, clean
selection, and high typical mass makes this cluster sample of particular
interest for cosmological analyses and studies of cluster formation and
evolution.
