It was donated this week to the museum by the American manufacturer, also based in Seattle.
Known as ZA003, the airplane was the third 787-8 produced by Boeing.
In donating the aircraft, the company cited its unique past.
Boeing said the ZA003 had circumnavigated the globe multiple times in 2011 and 2012, first as part of test and certification program and later during the Dream Tour, which introduced the 787 to the world.
“This revolutionary airplane caps the museum’s collection of historic commercial airplanes, beginning with our 1932 Boeing 247, which was the first all-metal, modern airliner,” said Doug King, president and CEO of the museum.
“It was followed by our 1969 prototype 747, the first jumbo jet, and now with the first composite airliner, the 787. It’s an incredible addition to our comprehensive display.”
One of the largest air and space museums in the world, the Museum of Flight attracts more than a half million visitors annually.
As of last month, Boeing had won orders for 1,050 Dreamliners from nearly 60 customers. More than 200 airplanes have been delivered so far.
Major Dreamliner operators include All Nippon Airways, Air India, Air New Zealand, Japan Airlines, Ethiopian Airlines and Air Canada.
Photo shows visitors waiting to see the Dreamliner at the museum Saturday. Courtesy: Boeing