At current prices, the order has an estimated value of $7 billion, according to a news release.
Boeing had already received orders for a total of 259 777X planes worth about $95 billion. The company says the 777X had the largest launch of any commercial jetliner in history last month at the Dubai airshow.
Boeing plans to deliver its first 777X aircraft in 2020.
Cathay Pacific is currently the second largest operator of 777-300ER planes.