The brief will involve conception and design of the fleet's premium economy and economy cabins, plus external branding on the aircraft's body and tailfins.
The holiday company is set to be the first operator of the 787 Dreamliner in the UK when it eventually rolls off the production line in 2009.
The First Choice head of marketing, Andrew Laurillard, said: "BMB has been a key partner in developing the brand over the past two years, and we're delighted that it will be helping to shape the experience on board our new aircraft."
The 787 Dreamliner is 20 per cent more fuel-efficient than similar-sized aircraft and has a 40-per-cent-reduced noise footprint. It can fly non-stop from the UK to locations as far as Hawaii, opening new destinations for the travel company.