B777 Captain reported while in cruise flight receiving a fuel disagree EICAS message resulting in the flight crew identifying a fuel leak then diverting to the nearest suitable airport.

Narrative

Flying east of position ZZZZZ we noticed our fuel calculations were trending into negative numbers. ATC had kept us lower than planned for tra'c although the numbers were still more than anticipated. We got a fuel disagree EICAS message and ran the checklist. That checklist then drove us to the fuel leak checklist. The relief officers were requested from break to the flight deck. We all ran the checklist together to work the problem to determine the leak. Dispatch and Maintenance Control were contacted as well. It was determined that the leak was in the right engine. The nearest suitable airport was ZZZ as we would be shutting down the right engine for the fuel leak. I notified the Purser and made a PA to the passengers. Coordination was made with ATC as we requested priority handling. Prior to landing We needed to dump fuel. Location; Altitude; Time and amount were noted and relayed to ATC. Fire rescue was requested and met the aircraft upon landing. Everything appeared normal with the aircraft upon landing by the fire rescue crew. We taxied to the gate and met with mechanics who quickly found the problem with the right engine. All passengers and crew safely deplaned and were processed through customs and immigration. A thorough debriefing was accomplished by the crew.