The massive jet took off bound for Cancun, in Mexico, as part of a new transatlantic service operating out of Glasgow.
Thomson Airways, the first UK airline to fly the new state-of-the-art aircraft, said the flight marked a key milestone.
The first flight left with 291 passengers on board.
The Dreamliner is set to revolutionise air travel thanks to improved on-board comfort and features which can reduce the effects of jet-lag.
It can also fly much greater distances than similar-sized aircraft and is more environmentally friendly, using 20% less fuel than previous planes.
Thomson Airways will fly the new aircraft from Glasgow on long-haul routes to Sanford, Florida and Cancun, and will add Punta Cana in the Dominican Republic to its service from summer 2014.
The aircraft will also operate out of from London Gatwick, Manchester and East Midlands airports.
Amanda McMillan, managing director of Glasgow Airport, said: "To be the first airport in Scotland to welcome the Dreamliner is a tremendous honour and something we're extremely proud of.
"Not only will the new aircraft offer passengers a unique flying experience, it will open up new possibilities for the long-haul market from Glasgow Airport and we are looking forward to working with Thomson to ensure the Dreamliner realises its full potential."
Scotland's Deputy First Minister, Nicola Sturgeon was at the airport to wave off the first flight.
She said: "It is exciting to see the 787 Dreamliner make its first flight and I am sure that all of those on board will have the best start to their holiday.
"We want to see more direct long-haul flights from Scottish airports and having this aircraft depart from Glasgow is very encouraging, especially as this aircraft is suited to routes from regional airports because of its long range."
And Renfrewshire Council Leader Mark Macmillan added: "Glasgow Airport has a proud history of pioneering aviation developments and this is another important milestone.
"The first flight of the Dreamliner in Scotland is a notable event in itself and, in the longer term, will boost travel options for passengers and strengthen the economic impact of Glasgow Airport."