The transient analysis of nuclear reactors is an important issue from a safety point of view. The deterministic methods, by considering different approximations, are extensively used to solve the neutron transport equations. Nowadays, by the continuous increase of computational resources, the feasibility of utilization of pure Monte Carlo methodology in the nuclear reactor transient analysis, without using different approximations, is being increased. In the present work, a detailed Dynamic Monte Carlo (DMC) methodology is developed and employed to investigate the transient analysis of source driven nuclear systems. Analytically solvable time and space and time dependent problems are introduced and solved to verify variance reduction tools used in the DMC methodology. Then, the DMC method is utilized to generate time dependent Green's functions for transient analysis of the source-driven systems (SDSs) studied in literature. The equilibrium and post perturbation transient responses of source driven systems are obtained by utilizing the Green's functions generated for those systems. The newly developed novel method is applied to different transient benchmark problems of SDSs. The performance and validity of the proposed method are discussed through qualitative and quantitative comparisons with the results given for the test and benchmark problems.