Boeing shares rose 1 percent to $136.68 in early trading on the New York Stock Exchange.
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The 777X, due for launch in 2020, will be a derivative of Boeing's top-selling wide-body plane with new wings and engines.
Cathay Pacific expects to take delivery between 2021 and 2024, the airline said.
Boeing started selling the 777X at the Dubai Airshow last month, where it garnered a record 259 orders and commitments worth $95 billion at list prices.
The company is yet to decide where to build the 777X, which is expected to be its only new jetliner program for the next 15 years along with the narrow-body 737 MAX jet due in 2017.
Union workers in Washington, where Boeing currently builds 777 planes, rejected a contract offer last month, leading the company to consider other places.
Cathay Pacific shares closed up 1.5 percent on the Hong Kong Stock Exchange.