Edinburgh's Hogmanay celebrations, which attracted 80,000 people, passed with only four arrests, police said.
A total of 350 officers patrolled Princes Street and the surrounding area, where revellers from across the world attended the annual street party.
Temperatures dropped to -6C and Madness and the Noisettes provided the music.
In Glasgow, 10,000 revellers packed into the city's George Square and were entertained by Deacon Blue and a fireworks display.
Heavy snow forced organisers to cancel the new year celebrations in Inverness.
Madness headlined the Concert in the Gardens in Edinburgh with lead singer Suggs appearing dressed in a spangly, checked suit to perform hits such as Baggy Trousers and One Step Beyond.
Noisettes lead singer Shingai Shoniwa ignored the chilly temperatures, ditching her jacket to dance in a white corset and skirt to sing Don't Upset the Rhythm.
Meanwhile crowds gathered at the esplanade of Stirling Castle saw in the new year with acts including Sandi Thom and the MacDonald Brothers.
Three stages along Princes Street provided entertainment by bands including Indie rockers We Were Promised Jetpacks and rock band The Enemy.
Traditional Scottish music was also on offer at The Keilidh.
Pete Irvine, creative director of Edinburgh's Hogmanay, described the atmosphere at the street party as "friendly and euphoric".
He said: "It has been an extraordinary night in Edinburgh with brilliant music, a magical fireworks display against a full moon sky and the dramatic castle slopes dotted with snow, and a friendly and euphoric atmosphere that you won't find anywhere else in the world."
Revellers heeded warnings to wrap up warm and many wore horned tartan helmets and furry Highland cow hats.
The street party is the highlight of a five-day Hogmanay Festival in Edinburgh, featuring a torchlight procession and dance and music events, which ends on 2 January.
Four people were arrested for breach of the peace and five people were treated in hospital for minor injuries.
Medical Director, NHS Lothian, Dr Charles Swainson, said: "Thousands of people have braved the cold weather to join in the festivities and the Hogmanay street party is one of the highlights of the year.
"I am delighted that the celebrations have gone well, and that most people have taken our advice by wrapping up warm, and drinking responsibly."
The Scottish Ambulance Service said Hogmanay was once again its busiest night of the year.
A spokesman said the service dealt with 2,247 calls to its 999 centres across Scotland between midnight and 0700 GMT on 1 January.
That was an increase of 5% on last year's total of 2,141 calls.
Arrangements were made for extra crews and control room staff to provide cover across the country and Edinburgh experienced the biggest increase with a 20% rise in call volumes.
In Aberdeen a fireworks display was held over His Majesty's Theatre at midnight, while the streets of Stonehaven, in Aberdeenshire, were lit up by the 150-year-old fireball festival.
Meanwhile the event in Inverness was cancelled as the weather deteriorated, making travel routes treacherous.
A large crowd had been expected in the city for the Red Hot Highland Fling - a free event with entertainment from cult bagpipe group The Red Hot Chilli Pipers and Celtic fusion band the Peatbog Fairies.
Northern Constabulary said they had rescued motorists stranded on the A9 southbound and urged people not to make unnecessary journeys.
Ch Insp Andrew MacLean, said: "The underfoot conditions in Inverness are extremely hazardous and the roads in the city and in the outlying areas are treacherous."
Meanwhile the closure of Inverness airport meant dozens of passengers had to find overnight accommodation in the city.
But 16 opted to stay in the terminal to bring in the new year with champagne and pizza.