The James Webb Space Telescope (JWST) will perform exoplanet transit spectroscopy in the coming decade promising transformative science results. All four instruments on board can be used for this technique which reconstructs the atmospheric transmission or emission spectrum of an exoplanet from wavelength-dependent light curve measurements. Astrophysical and instrumental noise and systematics can affect the precision and accuracy of the final spectrum, and hence, the atmospheric properties derived from the spectrum. Correlated noise and time-dependent systematics that can bias the measured signal must be accounted for in the final uncertainties. However quantifying these effects can be difficult with real data or simple analytic tools. Existing publicly-available simulators for JWST do not adequately simulate complex time domain processes on exoplanetary transit observations. We report JexoSim, a dedicated time domain simulator for JWST including all four instruments for exoplanet transit spectroscopy. JexoSim models both the astrophysics and the instrument, generating 2-D images in simulated time akin to a real observation. JexoSim can capture correlated noise and systematic biases on the light curve giving it great versatility. Potential applications of JexoSim include performance testing of JWST instruments, assessing science return, and testing data reduction pipelines. We describe JexoSim, validate it against other simulators, and present examples of its utility.