Distributed virtual environments (DVEs) are distributed systems that allow multiple geographically distributed clients (users) to interact simultaneously in a computer-generated, shared virtual world. Applications of DVEs can be seen in many areas nowadays, such as online games, military simulations, collaborative designs, etc. To support large-scale DVEs with real-time interactions among thousands or even more distributed clients, a geographically distributed server architecture (GDSA) is generally needed, and the virtual world can be partitioned into many distinct zones to distribute the load among the servers. Due to the geographic distributions of clients and servers in such architectures, it is essential to efficiently assign the participating clients to servers to enhance users' experience in interacting within the DVE. This problem is termed the client assignment problem (CAP) in this paper. We propose a two-phase approach, consisting of an initial assignment phase and a refined assignment phase to address the CAP. Both phases are shown to be NP-hard. Several heuristic assignment algorithms are then devised and evaluated via extensive simulations with realistic settings. We find that, even under heterogeneous environments like the Internet where accurate input data for the assignment algorithms are usually impractical to obtain, the proposed algorithms are still beneficial to the performances of DVE.