The All Nippon Airlines (ANA) flight will take off from Tokyo around 1230 local time, bound for Hong Kong.
The Dreamliner had originally been scheduled for delivery in 2008, but Boeing has suffered a string of setbacks.
Boeing plans to make 10 of the planes a month from 2013.
Wednesday's flight is a special charter, with normal services due to start in November.
Because of the materials used in construction, Boeing says the Dreamliner is about 20% more fuel efficient than similarly sized models flying today.
That would be a big help for airlines coping with the high cost of jet fuel, which is usually their biggest single cost.
Japan, a country in which Boeing dominates rival Airbus, is a major market for the Dreamliner.
ANA will take delivery of dozens more of the aircraft in the coming years.
But Boeing's delays have hurt its business.
Last week, China Eastern Airlines cancelled orders for 24 Dreamliners, rather than wait for production to pick up.

The League Two newcomers fell behind on 27 minutes when Joshua Mullin headed in a free-kick from Nicky Cadden.
Mullin then provided a neat cross for Daniel Mullen to knock in right on the stroke of half time.
Mikey Miller crashed a shot against the woodwork as the visitors from League One continued to dominate before Liam Buchanan made it 3-0 from close range.
Ousman See went close for the hosts but was denied a landmark goal by a smart save from Liam Kelly.
Livingston move up to second place in Group G, behind St Mirren, who have two wins from two.
After three years of delays, Boeing's Dreamliner jet is set for its maiden commercial voyage.
[NEXT_CONCEPT]
Edinburgh City's first competitive match as an SPFL side ended in League Cup defeat to Livingston at Meadowbank.