The nation's major wireless providers have agreed to a deal with the U.S. government to build a central database of stolen cellphones—part of a broad effort to tame an explosion of thefts nationwide.

The database, which the wireless companies will build and maintain, will be designed to track phones that are reported as lost or stolen and deny them voice and data service. The idea is to reduce crime by making it difficult or impossible to actually use a stolen device, reducing resale value.

Currently,...