A record £66 million Lotto jackpot will be shared between two tickets which matched the six winning numbers, Camelot said.
Each lucky winner will receive £33,035,323.
The main draw numbers were 58, 47, 27, 46, 52, 26 and the bonus number was 48.
The jackpot passed the £50 million cap on Wednesday and if no single ticket had matched all six main numbers, the huge sum would have rolled down to be shared among those tickets matching five main numbers and the bonus ball.
Instead, those five ticket-holders each win £64,426.
The 259 tickets which matched five main numbers each win £1,309 while 17,695 matched four numbers to win £123.
There was a £25 prize for the 418,225 players who matched three numbers.
A National Lottery spokesman said: "What an amazing way to start off the new year! Two players shared tonight's biggest-ever Lotto jackpot, and each ticket-holder will be starting 2016 £33 million richer.
"As well as the jackpot, as with every draw, the Lotto Millionaire Raffle created yet another guaranteed millionaire.
"We urge all our players to check their tickets and, of course, we have plenty of champagne on ice ready to welcome these winners into the National Lottery millionaires club.
"Remember, each and every ticket sold helps raise more money for Good Cause projects, totalling up to more than £34 million every single week."
The National Lottery website experienced some problems as an "unprecedented" number of last-minute buyers rushed to buy tickets.
Camelot said it expected to have sold at least 400 tickets per second, online and by retailers, in the final hours before sales stopped at 7.30pm on Saturday.
Noel Edmonds pushed the button to start the draw which used machine Guinevere to generate the numbers from set of balls six.
The Deal Or No Deal host, who presided over the first draw in November 1994, said he was "absolutely delighted" to take part in "another historic moment", especially as he had not been allowed to press the button to start the 1994 draw.
The jackpot rolled over 14 times before it reached the £50 million limit which meant it had to be shared out on Saturday, which was draw number 2,092.
The recent run of rollovers follows the number of balls in the draw increasing from 49 to 59 in October, reducing the odds on a player's six numbers coming up from around one in 14 million to one in 45 million.
Saturday's top prize eclipsed the previous highest jackpot of £42 million which was shared by three winners in 1996.
But it was still dwarfed by the 900 million dollar prize (£619 million) on offer in the US multi-state Powerball lottery - the largest jackpot in US history.
Wednesday's Lotto jackpot is an estimated £2.4 million.
Nobody won the Lotto Hotpicks jackpot which uses the same numbers as Lotto.
Thunderball's £500,000 top prize also went unclaimed after nobody matched five numbers and the Thunderball.
The numbers were 02, 03, 05, 22 and 11 and the Thunderball was 12.