B777 First Officer reported a fuel leak resulted in an engine shutdown and diversion.

Narrative

During cruise at FL350 we observed that our fuel burn was higher than anticipated. Fuel flows were within the normal range for both engines; but the #2 engine burned at a slightly higher rate than the #1 engine. A few minutes later; Dispatch sent us an ACARS message noting that the fuel burn appeared greater than expected. The Fuel Disagree EICAS message illuminated; and we accomplished the Fuel Disagree checklist. We selected the Totalizer fuel quantity and sent an ACARS maintenance entry for the Fuel Disagree EICAS.The difference between the Totalizer and Calculated fuel gradually increased; eventually reaching 17;000 lbs. The Fuel Disagree checklist drove us to the Fuel Leak checklist. The Relief Pilots were woken up from their break and summoned to the flight deck. All pilots collectively discussed the fuel leak and collaborated on a mutually agreed-upon course of action. Dispatch and Maintenance Control were contacted. Maintenance Control noted that there was no aircraft history of a fuel leak. The center tank fuel was exhausted. The fuel quantity in each tank; the difference in imbalance between the left and right fuel tanks; and the projected landing fuel quantity were recorded and evaluated every 15 minutes. The imbalance between the left and right fuel tanks gradually increased over the next hour to greater than a 1;000 lb. change within 30 minutes; per the Fuel Leak checklist. The projected landing fuel quantity for ZZZ gradually decreased to over 10;000 lbs. less than the planned remaining fuel. A First Officer was sent back into the cabin to inspect the wings and engines. No fuel spray or abnormalities were visually detected.All parties agreed that a diversion was appropriate. The nearest suitable airport was ZZZ1. The Captain informed the Purser of the diversion and made a PA to the passengers. Coordination was made with ATC. It was determined via the Fuel Leak checklist that the leak was in the #2 engine and that it was necessary to shut down the #2 engine. A fuel imbalance of approximately 3;000 lbs. was observed. Fuel was balanced via the Fuel Imbalance checklist. The APU was started.At FL190; approximately 30 minutes prior to landing; the #2 engine was shut down per the Fuel Leak checklist.At 13;000 ft.; we elected to jettison fuel to the maximum landing weight. Fuel jettison of approximately 24;000 lbs. was accomplished in approximately 7 minutes; with ATC coordination; via the Fuel Jettison checklist. The weather in ZZZ1 was marginal VFR with light winds. Runway XX was requested; as the winds favored this runway. A comprehensive briefing for the single-engine approach; including landing performance data and single-engine missed approach procedures; was discussed. An uneventful and stabilized single-engine approach to ILS Rwy XX in ZZZ1 was made by the First Officer; using flaps 20 and max autobrakes. The autopilot was disconnected at approximately 1;500 feet. After landing and once clear of runway XX at taxiway 1; emergency equipment inspected the aircraft on taxiway 2. No indications of fire or fuel leaking were found by emergency equipment personnel. An uneventful taxi via taxiway 1; 3; and 4 to gate XX was accomplished. After block-in; maintenance personnel came to the cockpit to notify the flight crew that the #2 engine had an observable fuel leak. The #2 engine fuel pump was subsequently replaced. All passengers and crew safely deplaned with emergency equipment standing by and were processed through customs and immigration. Ground transportation and hotel accommodations in ZZZ1 were made for all crewmembers. There were no reported injuries or aircraft damage. The flight crew and purser debriefed.