The exact role that bone marrow (BM)-derived endothelial progenitor cells (EPCs) play in tumor neovascularization is heavily debated. We develop a quantitative three-compartment model with predictive power regarding the dynamics of tumorigenesis. There are two distinct processes by which tumor neovasculature can be built: angiogenesis is the formation of new blood vessels from preexisting vessels; vasculogenesis is the formation of new vessels by recruiting circulating EPCs. We show that vasculogenesis-driven and angiogenesis-driven tumors grow in different ways. (i) If angiogenesis is the prevailing process, then the tumor mass (and volume) will grow as a cubic power of time, and BM-derived EPCs will stay at a constant level. (ii) If vasculogenesis is the dominant process, then the tumor mass will be characterized by a linear growth in time, and the number of circulating EPCs (after possibly increasing to a maximum) will decrease to low levels. With this information, one can identify the "signature" of each of the processes in the observations of tumor growth and the dynamics of the relevant characteristics, such as the level of BM-derived EPCs. We show how our results can help explain some apparently contradictory experimental data. We also propose ways to couple this study with directed experiments to identify the exact role of vasculogenesis in tumor progression.