The iPhone 5S is equipped with a fingerprint scanner and comes in limited edition gold, silver and ''space'' grey.
It is expected to fly off the shelves - but it is unclear whether the colourful 5C model will have the same reception.
The cheaper 5C comes in five hues - pink, blue, yellow, green, and white - and has been released at a time when Apple faces stiffer competition than ever before.
The scene in Glasgow was echoed across the country.
In London, hundreds of people streamed through the doors of Apple's flagship Regent Street store to get their hands on the phone.
Some began queuing outside the central London shop as early as Monday afternoon to buy Apple's latest model, the futuristic handset.
Noah Green, 17, was the first in the queue, having only left his vigil to shower at a nearby gym since setting up camp outside the store at 4pm on Monday.
Emerging from the store 20 minutes after the doors opened to rapturous applause, Noah, clutching a limited edition gold device, said: "It's the best feeling in the world.
"I'm the first in the United Kingdom and I have the best phone."
The teenager said he turned down offers of up to £5,000 for his prime spot in the queue, saying he would only consider giving up his place for £10,000.
Brother and sister Olly and Charlotte McIlroy, from Bexleyheath, spent more than £2,000 on four handsets for their family.
The pair, drawn to the 5S Touch ID technology which allows users to unlock their phone with the touch of a finger, said they had fun since joining the queue last night.
Charlotte, 19, said: "We thought it would be a really fun experience. We met some really nice people."
Olly, 16, added: "Our brother and mum are paying us £100 to do it."
The queue snaked around a packed Regent's Park, with several people carrying tents and energy drinks as they made their way towards the store from 8am.
Inside, Apple staff wearing blue T-shirts formed a makeshift guard of honour as the first customers made their way to the tills.
The two handsets were unveiled for the first time last week.
The 5S device, said to be twice as fast as its predecessor, is available through EE, O2, Three, Carphone Warehouse and Phones4u priced at £549 (16GB), £629 (32GB) and £709 (64GB).
The cheaper 5C - which marks Apple's first departure from premium phones - has been available for pre-order and is priced at £469 (16GB) and £549 (32GB).
Gavin Thomas, deputy editor of British-based iCreate magazine, said anticipation surrounding Apple releases had snowballed in recent years.
He said: "Apple have got a good, reliable brand where customers know what they are getting, straight off the bat.
"An Apple product launch is always an exciting time, and today was no exception.
"There was a lot of talk about the 'budget iPhone' this time around, too."
Latest findings from market research firm Kantar Worldpanel ComTech show Apple continues to perform well in the US where its IOS operating system has grown its share to 43.4% of sales.
In Britain it commands 31.1% of sales, behind Android, the operating system used on Samsung and HTC phones - with 55.2% of the market share.
Mr Thomas said: "Apple keeps following the winning formula in its products, so it's hard to think of them losing a share in the market."