The South Korean technology giant said it had experienced 'stronger than expected' pre-orders for the new flagship devices.
Some customers who ordered early were expected to receive their new devices before the official sales launch today in South Korea, the US, the UK and other markets.
Samsung is hoping the new phones, which feature a 5.5 inch (14cm) wrap around screen in the S7 Edge and a 5.1 inch display in the S7, can revitalise its phone sales.
While the Galaxy S6 saw the company experience a surge in phone sales, it has faced increasing competition from cheaper devices like Motorolas Moto X Style and Huaweis Honor 7.
Samsung is particularly keen to see sales in China being revived by the S7 as it has been lagging behind competitors in what is now the world's biggest smartphone market.
Koh Dong-jin, president of Samsung's handsets business, did not give a figure for pre-sales of the phone but said they had been 'stronger than expected'.
Speaking at the launch of the phone last month, DJ Koh, president of mobile communications at Samsung Electronics, said: 'We believe in a world that is brighter, sharper, more convenient, and more fun.
'We strive to deliver on that vision with the Galaxy S7 and Galaxy S7 edge by marrying elegant design with functionality and providing a seamless mobile experience.
'We empower consumers with technology to help them get more out of life and will continue to push the frontier of what's possible.'
The Galaxy S7 costs £569 in the UK for the 32GB device and will come in either black or gold, while the 32GB S7 Edge costs £639.
However, many networks are offering the devices as part of mobile contracts for around £34.
While the S7 devices feature a handful of new features, they also bring back some that many customers felt were missing from the S6 but had been in previous models.
The devices will be water resistant and also feature expandable memory through a micro-SD card slot which can add an additional 200GB of memory.
Each device is apparently able to withstand up to 30 minutes under 5ft (1.5 metres) of water, meaning it should be able to survive an accidental dip into a puddle, or even being dropped down the toilet.
The devices will also feature the first Dual Pixel camera in a phone to deliver 'brighter and sharper images' in low light, according to Samsung.
The phones have been well received by reviewers with many commenting that the curved glass sides of the S7 Edge help to make the device a slimmer and more compact phone to use.
Although the 'always-on' feature is new to Samsung handsets, the Nexus 6P and Motorola Moto X both use always-on ambient displays.
The ambient display works by only showing the pixels that are needed to display a particular notification at the top of the screen.
For instance, when a notification arrives, it appears in black and white on a small portion on the S7 and S7 Edge's screen, meaning the phone doesn't have to use its battery's energy powering up all of its pixels.
'We know that people check their phones on average 85 times a day,' said Samsung's Vice president of brand and product marketing, Europe, Rory O'Neill.
Samsung has also unveiled a range of accessories for the S7 phones, including covers that allow users to see the clock on the screen through them and a case that features a keyboard.
Samsung said the S7 Edge will be able to perform for 13 hours while playing non-stop video content - for example, a whole series of Game of Thrones.
The firm said those who pre-order the handsets in Europe will receive a free Gear VR headset.
At the launch Mark Zuckerberg took to the stage to talk about the phones, virtual reality and Facebook, saying his company is committed to VR for the long-term.
'Going back about 10 years, most of what we shared and experienced was text,' he said.
'And then it was photos. And now we're entering into a world where that's video.
'But pretty soon we're going to live in a world where everyone has the power to share and experience whole scenes as if you're right there in person.
'There are lots of other challenges that we need to solve to create great VR experiences. Facebook, with Oculus, are committed to this for the long term...
'VR is going to be the most social platform... Gear VR is by far the best mobile VR experience.