Two-neutrino double electron capture (\(2\nu\)ECEC) is a second-order Weak process with predicted half-lives that surpass the age of the Universe by many orders of magnitude. Until now, indications for \(2\nu\)ECEC decays have only been seen for two isotopes, \(^{78}\)Kr and \(^{130}\)Ba, and instruments with very low background levels are needed to detect them directly with high statistical significance. The \(2\nu\)ECEC half-life provides an important input for nuclear structure models and its measurement represents a first step in the search for the neutrinoless double electron capture processes (\(0\nu\)ECEC). A detection of the latter would have implications for the nature of the neutrino and give access to the absolute neutrino mass. Here we report on the first direct observation of \(2\nu\)ECEC in \(^{124}\)Xe with the XENON1T Dark Matter detector. The significance of the signal is \(4.4\sigma\) and the corresponding half-life \(T_{1/2}^{2\nu\text{ECEC}} = (1.8\pm 0.5_\text{stat}\pm 0.1_\text{sys})\times 10^{22}\;\text{y}\) is the longest ever measured directly. This study demonstrates that the low background and large target mass of xenon-based Dark Matter detectors make them well suited to measuring other rare processes as well, and it highlights the broad physics reach for even larger next-generation experiments.