But hundreds of people took to Twitter to say that many stores had ran out of the new devices, while Apple's online store pushed back its dispatch date for new phones to October, without giving any specific dates.
Technology fans in Japan were among the first to get the top-of-the-range iPhone 5S, as well as the new 'budget' version, the 5C.
Apple stores in the UK also opened early, at 8am, with estimates of 1,500 people outside one London store.
Staff at many of the shops had worked through the night to prepare for launch.
Devotees of the technology company started queuing at London's Regent Street branch on Monday, with Westminster Council forcing some to take down temporary shelters.
Gad Harari, 17, from north London, told Sky News he had been offered hundreds of pounds for his place at the head of the queue.
Some Apple fans outside a Tokyo store took things even further - reportedly beginning their wait a full 10 days before today's launch.
"I am super happy," said the first customer to buy a 5S at the Tokyo store.
"The first thing I want to do is to try out the finger print recognition function, that is what I looked for the most."
The premium 5S device, said to be twice as fast as its predecessor, sets itself apart from competitors with its Touch ID feature, which allows users to unlock their phone with the touch of a finger.
However, UK phone networks reportedly have very low stock levels of the new handsets, particularly the 5S.
On Twitter, @RealSandyPitt wrote: "iPhone 5S gold-coloured version sold out during the morning at Regent Street in London."
Meanwhile @Gromlus wrote: "Oh wow the iPhone 5S got sold out in two hours here at Arndale in Manchester."
Technology analysts also have reservations about the brightly-coloured plastic 5C model.
Seen as an attempt to gain a bigger foothold in markets such as China, it has been criticised as "nowhere near" cheap enough to gain significant market share in the country.
In the UK, 5S prices start at £549, while the cheaper 5C phone costs from £469. A 64 gigabyte model comes in at a hefty £709.
In comparison, the flagship model from rival HTC costs £484 and Samsung's top-of-the-line Galaxy S4 is around £420.
Apple will be hoping the updated devices give it new momentum in the worldwide smartphone market, which is increasingly dominated by cheaper handsets running the Android operating system - particularly those by market leader Samsung.
Today's launch may also provide a distraction from criticisms of new operating system iOS 7.
Many users reported problems downloading the update when it launched earlier this week and several security flaws have also been exposed.
One flaw allows someone to access photos and videos, even when a iPhone or iPad has been locked. The media can then be deleted or shared.
Another glitch in iOS 7 allows a potential thief to bypass the Find my iPhone feature by putting the device in airplane mode to stop it communicating its location.
Apple is expected to fix the issues in a future update.
The new iPhones go on sale today in the US, Australia, China, Canada, France, Germany, Singapore and UK. Other countries will follow.
More From Sky News