"It is a new era for two global brands that will help us in our quest for new triumphs," club president Florentino Perez told a news conference at the Bernabeu stadium on Thursday.
"It is one of the most important agreements in the history of the club," said the construction magnate who is likely to be returned to the presidency unopposed next week as no rival candidates have yet challenged him in an election.
No official figures were released for the sponsorship deal which is reported by media to be worth up to 30 million euros a year.
Madrid's famous white strip will carry the slogan 'Fly Emirates'.
The Dubai-based carrier replaces online betting firm bwin who have sponsored Real's shirts for the last six years in a deal that was reported by consulting firm Sport+Markt to be worth around 23 million euros a year.
On Tuesday, the club said bwin will become their official digital partners in a new multi-year deal as the company switches its strategy to focus on social media, gaming and the integration of online with mobile useage.
The airline deal brings Real closer to arch rivals and La Liga champions Barcelona who have a shirt sponsorship agreement with the Qatar Foundation worth around 30 million euros a season until 2016.
Last season Real became the first football club to pass the income threshold of 500 million euros, according to Deloitte's Football Money League ranking published in January.
Their earnings of 513 million euros beat Barca into second place on 483 million, with Manchester United a distant third on 396 million.
Last year United announced a new sponsorship deal that will see General Motors's Chevrolet brand on their red shirts from 2014 in a seven-year deal worth $559 million - the most lucrative such sponsorship in football.
Real will finish the 2012/13 campaign on Saturday without a major trophy this season as they came second in La Liga, fell in the Champions League at the semi-final stage and lost the King's Cup final to city rivals Atletico Madrid two weeks ago.
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