A novel approach is presented for the reconfiguration of satellite constellations based on Lambert’s theorem. The reconfiguration problem, in this article, is considered with the constraint of overall fuel cost minimization. Hence, orbital maneuvers required for the operation of reconfiguration is designed in such a way that, transferring the satellites to the desired configuration of constellation will be possible at minimal cost. Also, the introduced method of orbital transfer for implementing the reconfiguration phase of satellite constellation has no limitation on the shape and orientation of initial and target orbits such as: co-planarity, coaxiality, circularity and/or the existence of a common point. Moreover, a method is offered for modeling the cost function of reconfiguration problem in which the two important tasks of optimal orbital transfer of satellites to the target configuration of constellation and optimal assignment of each satellite to a specific terminal position or final orbit will be done in one single step. For this purpose and in order to achieving the globally optimal solution of the reconfiguration problem of constellation the hybrid PSO/GA is used. Finally, two different scenarios of reconfiguration of satellite constellation will be modeled once by the presented approach and once by considering determined positions of flight and deployment for the satellites. The obtained results indicate the superiority of the idea presented in this article.