The baseline 777-200 was certified with all three engine types - PW4000/112", GE90, and RR Trent 800. When Boeing went to the 777-300 and -200ER, the engines were basically unchanged, just operated to higher ratings than the original.
During development of the 777-300ER/200LR, Boeing decided that the market was too small for all three manufactures to develop a 115k thrust class engine, and chose GE's proposal as sole source to upgrade the GE90. So the only engine available for the very high gross weight 777-300ER/200LR is the GE90-115B.
Note that the GE90-115B is quite a bit different than the GE90-94B series on other 777s - basically the -115B has an all new LP section as well as changes to the HP.