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The entry of the coronavirus SARS-CoV-2 into human lung cells can be inhibited by the approved drugs camostat and nafamostat. Here we elucidate the molecular mechanism of these drugs by combining experiments and simulations. In vitro assays confirm that both drugs inhibit the human protein TMPRSS2, a SARS-Cov-2 spike protein activator. As no experimental structure is available, we provide a model of the TMPRSS2 equilibrium structure and its fluctuations by relaxing an initial homology structure with extensive 330 microseconds of all-atom molecular dynamics (MD) and Markov modeling. Through Markov modeling, we describe the binding process of both drugs and a metabolic product of camostat (GBPA) to TMPRSS2, reaching a Michaelis complex (MC) state, which precedes the formation of a long-lived covalent inhibitory state. We find that nafamostat has a higher MC population than camostat and GBPA, suggesting that nafamostat is more readily available to form the stable covalent enzyme-substrate intermediate, effectively explaining its high potency. This model is backed by our in vitro experiments and consistent with previous virus cell entry assays. Our TMPRSS2-drug structures are made public to guide the design of more potent and specific inhibitors.