The 'Link, Like, Love' app provides cardholders with a personalised dashboard of deals, content and experiences based on their - and their friends' - Facebook likes and interests.
Cardholders choose the deals they want and Amex automatically sends 'statement credits' to their account. To claim the deal, users just pay with their card, online or in-store, as normal without having to present a physical coupon.
Amex says its technology also enables it to provide merchants with detailed reporting on deal redemption and customer loyalty to help them design their marketing programmes.
The card firm has also developed a marketing tool for merchants called 'Go Social' to help them create and distribute coupon-less offers for Facebook and other digital channels such as Foursquare, with which Amex struck a deal deal earlier this year.
Among the merchants signed up to the app so far are 20th Century Fox, Dunkin' Donuts, Whole Foods Market and Virgin America.
Ed Gilligan, vice chairman, Amex, says: "As we continue to transform our business in the digital space, we're focused on three key areas: value, relevance and user experience, for both cardmembers and merchants. Because of our unique business model - our closed loop - we're able to deliver on all three in a way that is unprecedented."