SEOUL—South Korea will allow one of its largest companies to build a new organic light-emitting diode production facility in China, the first time a Korean firm will transfer the sophisticated technology abroad.

Tuesday’s approval by Seoul’s trade ministry is the latest sign that relations between the two countries are improving after a summit between their leaders to restore economic links—and coordinate policy on North Korea—earlier this month. South Korea this year deployed a U.S.-made missile defense battery, triggering a diplomatic dispute that hampered regional efforts to respond to Pyongyang.

The approval could lead LG Display Co. LPL -0.93% , one of the world’s biggest makers of display panels used in smartphones and televisions, to cement its global market dominance for large OLED panels. The company has said it plans to invest 5 trillion South Korean won, or $4.7 billion, in China by 2020—a quarter of its OLED investment over the next three years—citing cheaper costs. It aims to begin its OLED production in China in 2019.

LG Display has also said it plans to boost its OLED production to some 2.8 million units next year, up 1.1 million from 2016. In July it announced plans to start producing the panels in the Chinese city Guangzhou, adding to existing production there of less-advanced displays.

South Korea’s Ministry of Trade, Industry and Energy on Tuesday cautioned LG Display to increase security measures to protect the technology. South Korea’s government has restricted overseas export of some of its valuable industrial technology, including OLED, to keep local industries more competitive than their foreign rivals.

Under South Korean law, companies are required to seek government approval to export such technologies.

China’s BOE Technology Group Co. has spent at least $17.7 billion to ramp up its OLED production in recent years. Though its production quality lags behind its more sophisticated South Korea competitors, IHS Markit estimates that it will become the world’s largest display manufacturer by volume by 2019.

Tuesday’s decision is likely to boost LG Display’s chances of maintaining its top position in the large-model OLED market—while expanding its capacity to make smaller screens, a market that has grown in recent years as more smartphone makers adopt those displays.

Write to Kwanwoo Jun at kwanwoo.jun@wsj.com and Eun-Young Jeong at Eun-Young.Jeong@wsj.com