We present a catalog of 4195 optically confirmed Sunyaev-Zel'dovich (SZ) selected galaxy clusters detected with signal-to-noise textgreater 4 in 13,211 deg$^2$ of sky surveyed by the Atacama Cosmology Telescope (ACT). Cluster candidates were selected by applying a multi-frequency matched filter to 98 and 150 GHz maps constructed from ACT observations obtained from 2008-2018, and confirmed using deep, wide-area optical surveys. The clusters span the redshift range $0.04 \lt z \lt 1.91$ (median z = 0.52). The catalog contains 222 $z \gt 1$ clusters, and a total of 868 systems are new discoveries. Assuming an SZ-signal vs. mass scaling relation calibrated from X-ray observations, the sample has a 90% completeness mass limit of $\textrm{M500c} \gt 3.8 \times 10^{14}$ M$_\odot$, evaluated at z = 0.5, for clusters detected at signal-to-noise ratio textgreater 5 in maps filtered at an angular scale of 2.4'. The survey has a large overlap with deep optical weak-lensing surveys that are being used to calibrate the SZ-signal mass-scaling relation, such as the Dark Energy Survey (4566 deg$^2$), the Hyper Suprime-Cam Subaru Strategic Program (469 deg$^2$), and the Kilo Degree Survey (825 deg$^2$). We highlight some noteworthy objects in the sample, including potentially projected systems; clusters with strong lensing features; clusters with active central galaxies or star formation; and systems of multiple clusters that may be physically associated. The cluster catalog will be a useful resource for future cosmological analyses, and studying the evolution of the intracluster medium and galaxies in massive clusters over the past 10 Gyr.
          
          
          
            
            
            
            
            
              
              
              
                
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              Astrophysics - Cosmology and Nongalactic Astrophysics