Chris Weir said she and her husband Colin were "tickled pink" when they realised they had scooped Tuesday's jackpot.
"I even had a glass of white wine which is something I normally only do at Christmas!" laughed Chris.
The prize was Europe's biggest ever and was capped after a series of rollovers.
On the night of the draw Chris was checking their numbers on the BBC's Red Button digital text service about midnight on the television in their bedroom.
"I started circling the numbers I had matched but wasn't doing very well. Then on the fifth line, all the circles seemed to join up."
The telephone line run by Camelot for claims was closed. Chris and husband Colin sat up all night they were so excited.
"When we first realised we had won, it felt like a dream," Colin said. "Everything went into slow motion."
Life changing
When asked at a media conference in Falkirk what they will do with the money, Chris said: "We're not flashy people."
"The next steps are going to be the most difficult... with great wealth comes great responsibility," added Colin.
The Weirs have both had serious health conditions in recent years and have not been able to work.
Colin, 64, had previously worked as a television cameraman and Chris, 55, is a fully-trained psychiatric nurse.
The most exciting aspect of their windfall is the opportunity to travel.
"We have both always wanted to see the Great Wall of China and Colin would love to stand at the foot of Ayers Rock in Australia," said Chris.
"We also love art galleries, so this gives us the chance to visit those in Paris and in Russia. These are all things we thought we would never see."
They have also already decided to buy homes for their two children, Carly and Jamie (both in their 20s).
UK winning streak
Before Tuesday's draw, the largest lottery winner in the UK was the player who claimed £113m in the Euromillions last October and chose to remain anonymous.
The couple have displaced former postal worker Angela Kelly from East Kilbride, who became Scotland's biggest winner in August 2007 when she scooped £35,425,411.80 in the Euromillions jackpot.
Britons have banked the Euromillions jackpot more than 14 times in the last two years.
Last year, two anonymous UK winners scooped £113m and £84m.
And Nigel and Justine Page, from Gloucestershire, won the £56m jackpot prize on EuroMillions in February 2010.
National Lottery operator Camelot runs the Euromillions draw in the UK and has also had the same role for the weekly Lotto draw since it was launched in 1994.
The firm says that its draws have created about 2,400 lottery millionaires in the UK in the intervening 17 years.
If the winner of Tuesday's draw had been a single player, he or she would instantly have been placed 430th in this year's Sunday Times Rich List just above Scottish businessman Sir Angus Grossart and Irina Abramovich, the former wife of Russian oligarch Roman Abramovich.
Two other UK-based lottery players won £1.7m after they successfully matched five numbers and one Lucky Star.
A couple from Largs in Ayrshire have been named as the winners of the £161m Euromillions jackpot.