MANILA—The U.S.-China technology war is raging around the world, but the Philippines is no longer torn. It is binding its telecommunications future to China’s.

The country got its first taste of next-generation 5G services in late June with gear supplied by Huawei Technologies Co. This month, a new carrier backed by state-owned China Telecommunications Corp. will begin rolling out a network largely designed in China, to be executed by Chinese engineers in the Philippines.

The...