Designed from scratch in an operation dubbed "Project Zero", the Galaxy S6 and its curved-edges variant are critical for Samsung's plans to reverse plunging smartphone revenues that led to its first annual earnings fall in three years in 2014.
By some estimates, Apple surpassed Samsung as the world's biggest smartphone maker late last year, selling a record 74.5 million iPhones in the December quarter on the back of the success of its big-screen iPhone 6 and 6 Plus.
Samsung's previous flagship Galaxy S5 was outsold in its second full month of global sales by Apple's older iPhone 5S, according to researcher Counterpoint.
The South Korean giant begins its fight-back on April 10 when the revamped Galaxy phones, unveiled at the Mobile World Congress in Barcelona on Sunday, hit the market in one of the most important product launches in the company's history.
Samsung is yet to disclose pricing or where the phones will appear first.
Stand-out features include casing made from light-weight metal used in airplanes, a step up from the plastic that disappointed many critics of the S5, and Corning Inc's Gorilla Glass on both front and back.
The Galaxy S6 upgrades the previous version's camera and screen, and strips out many of Samsung's unpopular in-house software apps that infuriated users by gobbling memory.
In another departure, they have non-removable batteries to make them slimmer.
To compensate for the lack of interchangeable batteries, Samsung says a 10-minute charge by cord gives four hours of power.
Samsung is also touting the Galaxy S6's compatibility with a new mobile payments system it is preparing to launch in the United States and South Korea in the second half of this year, using the technology of recently acquired start-up LoopPay.
The system, in partnership with banks and credit card companies including MasterCard and Visa, will allow users to make mobile payments through magnetic strip-card readers without the additional accessory needed for other models.
The rival Apple Pay system, launched in the United States in September and rapidly winning retailer support, requires the installation of in-store near-field communication technology.
The new Samsung flagships will also come with free two-year, 115-gigabyte cloud storage through Microsoft Corp's OneDrive, suggesting improved relations between the firms after they settled a patent dispute last month.