The large, illuminated crystal ball was lowered for the last minute of the passing year - a tradition started in 1907.
Fireworks then filled the sky at midnight and confetti dropped on revellers in the square.
Around one million people attended the celebrations, which end a year of troubled economic times for the US and the 10th anniversary of the September 11 attacks.
"There's no doubt that 2012 will bring even more change," US President Barack Obama said in his end-of-year address.
"And as we head into the New Year, I'm hopeful that we have what it takes to face that change and come out even stronger."
Across South America the fireworks continued - in Rio de Janeiro, an estimated two million white-clad partygoers watched a spectacular "green" fireworks extravaganza on Copacabana beach.
In Berlin, another spectacular display lit up the night sky with partying at the Brandenburg Gate, while in Paris some 360,000 people flocked to the Champs-Elysees.
In Kiev, there was a football-themed countdown before fireworks lit up Independence Square. Ukraine will co-host Euro 2012 with Poland.
In the Egyptian capital, there were no pyrotechnics - instead the assembled masses in Revolution Square held a candlelit vigil to remember all those who had lost their lives during the Arab Spring of 2011.
Earlier, Sydney and Hong Kong set the New Year's Eve standard with glittering extravaganzas.
Sydney's famous harbour exploded in a blaze of colour on the stroke of midnight Down Under.
"Every year we make sure our celebrations are bigger and better than the one before," Sydney Lord Mayor Clover Moore said.
In Hong Kong, a barrage of fireworks was fired from several of its iconic buildings, delighting partygoers crammed on to the waterfront and in pleasure boats.
The mood was more sombre in Tokyo, but Dubai led the way in the Middle East.
The city's Burj Khalifa skyscraper, the world's tallest man-made structure, hosted a pyrotechnics display even more extravagant than 12 months ago.
Hundreds of thousands of people have taken to the streets of London and Edinburgh as parties and fireworks displays across the UK welcomed the start of 2012.
In London, crowds jostled along the banks of the River Thames for prime vantage points.
About 250,000 people were estimated to be in the English capital to watch the 11-minute and 15-second display, featuring some 12,000 fireworks.
There were 30 tons of equipment aboard three barges on the river ready for the display, which was triggered by GPS to the chimes of Big Ben.
It started with explosions blasting from the top of Westminster's landmark clock tower and went on to turn the London Eye into a gigantic Catherine wheel before culminating in a dazzling finale.
Sky News reporter Rhiannon Mills, watching from the bank of the Thames, described it as "incredible" and said it had "certainly lived up to expectations".
She added the Olympic rings had been depicted as part of the display and the television pictures beamed around the world would send a strong message that Britain was gearing up to stage a spectacular Games in the summer.
Mayor of London Boris Johnson said: "Our New Year fireworks were a brilliant start to a spectacular year.
"This is just the beginning - as the eyes of the world turn to London for the Olympic and Paralympic Games, there will be amazing events across the capital up to, during and beyond a summer like no other."
Big crowds were also seen in other cities, including in Edinburgh for the Hogmanay street party attended by some 80,000 people.
More than 20 acts were playing on seven stages ahead of the display, with Primal Scream performing their album Screamadelica.
Sky News correspondent James Matthews, having watched alongside revellers in the Scottish capital, said it had been "something to rival anywhere else".
"It was the longest that has ever been done here and the centrepiece was simply fantastic," he said.
Sean Ingles, 23, travelled from New Orleans in Louisiana to bring in the New Year in Edinburgh.
He said: "I came with my dad who is originally from here, he moved to the States about 25 years ago and he brought us home for the good times.
"The atmosphere is brilliant, I feel right at home. New Orleans is such a friendly city and Scotland is very much the same. It was definitely worth the trip."
Organisers hailed the night a success.
Pete Irvine, creative director of Edinburgh's Hogmanay, said: "Edinburgh's Hogmanay has a worldwide reputation, and we are delighted that, once again, revellers have travelled from around the globe to join us."
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