Cell mobility plays a critical role in immune response, wound healing, and the rate of cancer metastasis and tumor progression. Mobility within a three-dimensional (3D) matrix environment can be characterized by the average velocity of cell migration and the persistence length of the path it follows. Computational models that aim to predict cell migration within such 3D environments need to be able predict both of these properties as a function of the various cellular and extra-cellular factors that influence the migration process. A large number of models have been developed to predict the velocity of cell migration driven by cellular protrusions in 3D environments. However, prediction of a cell’s path persistence is a more tedious matter as it requires following a simulated cell’s path for a long time while it migrates through the model extra-cellular matrix (ECM). This is a computationally expensive process as it requires computing cell-matrix interactions in 3D and only recently, there have been attempts to quantify cell persistence as a function of key cellular or matrix properties. Here, we propose a new stochastic algorithm that can simulate 3D cell migration occurring over days within a simulation time of minutes, opening new possibilities of testing and predicting long-term cell migration behavior as a function of a large variety of cell and matrix properties. The fundamental property of the proposed algorithm that makes rapid simulations possible is that the matrix elements are generated on the go and stochastically based on the biophysical and biochemical properties of the ECM as the cell migrates through the 3D environment. Using this algorithm, we can study the effect of various cellular and matrix properties such as cell polarity, cell mechanoactivity, matrix fiber density, matrix stiffness, fiber alignment and fiber binding site density on path persistence of cellular migration and the mean squared displacement of cells over long times.