The announcement seals a deal first announced in 2007. It includes a firm order for Trent 900s to power 12 of the four-engine A380s with a potential for seven further options, and Trent 1000 engines to power two dozen of the twin-engine Boeing 787 Dreamliners with 18 options. The contract also includes long-term support.
Rolls-Royce said the value of the deal at list prices, including options, was potentially more than $5 billion.
The engine maker's shares were up 1.8 percent at 666 pence in early trading on the London Stock Exchange, above the 653 pence per share price just before the Qantas incident.
BA says the first of its A380s is due for delivery in 2013.
A Trent 900 disintegrated on a Qantas A380 on Nov. 4, shortly after takeoff from Singapore. The plane landed safely, but the engine failure was the most serious safety incident involving the world's biggest jetliner since it entered service in 2007.
Qantas grounded all six of its A380s for 19 days, but all have returned to service.
Rolls-Royce has upgraded engines of the same model as the Qantas engine, replacing a part which has been identified as the most likely cause of the problem.
Airbus, meanwhile, announced Thursday that Asiana Airlines of South Korea had placed a firm order for six A380s, with delivery to begin in 2014. Asiana did not immediately announce an order for engines.
It was the second A380 deal announced since November.
Skymark Airlines of Japan signed a memorandum of understanding on Nov. 12 to purchase four of the aircraft, but did not specify its choice of engines.
Airbus says its has booked 240 orders for the A380, with 40 delivered through December. Rolls-Royce says nine customers have chosen the Trent 900 for their planes.
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