The first flight from Airbus's base in Toulouse kicks off a 1400-hour flying test programme for the aircraft, which is expected to gain certification in mid-2018 with the first of the new aircraft going into service with Portugal's TAP.
Rolls president Eric Shulz described the flight as "a great moment for Airbus and Rolls-Royce".
Rolls's Trent 7000 engines are some of the biggest the company has ever produced, with the fan at the front measuring 3m across and sucking in 1.3 tonnes of air every second at take-off.
The news came as Boeing announced it had been given the green light from planners to build a giant hangar at Gatwick airport to service aircraft for its European customers.
The £88m ($187m) project is expected to create 100 jobs directly and support about the same number again.
The project is part of a pact between Boeing and the UK government for the US aerospace giant to increase its footprint in Britain as the country increasingly turns to Boeing for military equipment.
Recent purchases include a £2bn deal to buy nine P-8 Poseidon spyplanes and a similar value order for 50 Apache attack helicopters.
As part of the arrangement Boeing has pledged to build a £100m base at RAF Lossiemouth in Scotland to support the P-8, and the company is also constructing a factory in Sheffield, its first component manufacturing plant in Europe.
There have been fears that the pact could be threatened by the row between Boeing and Bombardier. Boeing successfully argued for 300 per cent trade duties to be imposed on C Series airliners built by the Canadian company that were sold in the US.
Boeing said the aircraft had been "dumped" on the US market and that the programme had been funded by illegal state subsidies.
Bombardier has almost 5000 staff in Northern Ireland, with about a quarter of them working on the C Series, and the tariffs raised fears over the future of their jobs if the levies hit production of the C Series. The UK Government had also hinted it might review future orders from Boeing in the wake of its actions against Bombardier.
Earlier this week, Airbus swooped in and took control of 50 per cent of the C Series programme, with promises to build the airliner at its Alabama base, in a move that is likely to circumvent the tariffs.