  We present a catalog of 4195 optically confirmed Sunyaev-Zel'dovich (SZ)
selected galaxy clusters detected with signal-to-noise > 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 < z
< 1.91 (median z = 0.52). The catalog contains 222 z > 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 M500c > 3.8 x 10$^{14}$ MSun, evaluated at z = 0.5, for clusters
detected at signal-to-noise ratio > 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.
