The Doha-based company, owned by the energy-rich Gulf state, has ordered 80 of the planes, making it not only the launch customer but also the largest single customer of the fuel-efficient A350 so far.
Qatar Airways's first A350 had been due to be delivered on December 13 in the southwestern French city of Toulouse where Airbus is based, but the airline postponed the handover at the last moment, citing equipment in the cabin that did not correspond to its requirements.
"My dear Akbar, you are a demanding customer, particularly demanding and sometimes even a little too demanding, but you are also one of the architects of the A350," Airbus chief Fabrice Bregier told Qatar Airways head Akbar al-Baker at the ceremony.
"We owe you a lot for this programme."
FUEL SAVINGS CRUCIAL
Airlines are in a major push to modernise their fleets to reap the energy savings that the latest generation of planes offer, especially as competition in the sector is fierce and fuel is one of biggest costs.
For the moment, Boeing dominates the lucrative market for long-haul, mid-sized planes with its B777 and next-generation 787 Dreamliner outweighing the European firm's A330.
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But Airbus hopes to catch up with its A350, whose wings and fuselage are made of carbon fibre and which will save up to 25 percent in fuel consumption.
Airbus invested 10-12 billion euros ($12-$15 billion) in its strategy to position the A350 between the popular B777 and the Dreamliner, hoping to eat away at both planes' markets.
So far, the plane has been a success with 778 orders already registered by the end of November.
Boeing, meanwhile, has accumulated 1,055 orders for the Dreamliner, which was launched several years ago.
The first commercial flight of Qatar Airways's brand new plane will take place on January 15 on the Doha to Frankfurt route, and the second A350-900 should come into operation in February.
The airline is one of a trio of fast-growing Gulf carriers seeking to further muscle into European markets, as energy-rich states in the region seek to develop new sources of income to reduce their dependence on oil.
Baker has described the delivery of the A350 as the "second significant fleet milestone" for the carrier after recently receiving three of 14 A380 superjumbo planes bought from Airbus.
The airline has also purchased Boeing's 787 Dreamliner.
The A350 programme was launched in 2007, and the first test flight for the plane took place in June last year.
Bregier told reporters in Toulouse that Airbus planned to ramp up production of its newest plane from two to 10 aircraft a month within four years.