Low earth orbit (LEO) satellite networks are capable of providing global or regional mobile services for a large number of users. Since the user's service duration may be greater than the coverage time of a LEO satellite, the user may be handed over to another visible satellite to prevent interruption of the ongoing communication. On the other hand, a mobile user may be covered by more than one satellite at the instant of connection handover. When the user is about to be handed over to another satellite, the serving satellite minimizing the number of handovers would in general be the one that provides the largest service time which is not necessarily equal to the coverage time of the very satellite. In this paper, we propose a new handover algorithm which exploits both the Global Positioning System (GPS) infrastructure and satellite diversity to provide a simple and real-time handover management in LEO satellite networks. The proposed algorithm not only minimizes the expected number of satellite handover, but is also efficient and easy to be implemented in hand-held devices, thus facilitating the mobile users' access to the satellite networks. Numerical simulations performed for two typical mobile satellite networks, viz. Iridium and Globalstar, corroborate the advantages gained by the proposed algorithm.