Organisers said it was the world's biggest rendition of Robert Burns' poem, which is sung around the globe at New Year. It was arranged to mark the 250th anniversary of Burns's birth.
Earlier, dance act Groove Armada and singer Paolo Nutini were the big names performing at the city's Concert in the Garden event.
Scots rockers Glasvegas and electropop group Hot Chip also played on live stages at the world-famous street party.
After opening the celebrations in the capital, Paisley-born Nutini travelled to Glasgow to headline the city's Hogmanay celebrations in George Square, where he was joined on the bill by another home-grown act, Idlewild.
Creative director of Edinburgh's Hogmanay, Pete Irvine, said: "We've tried a big thing with Auld Lang Syne and put on a great show tonight.
"Here in Edinburgh we have the arena and the backdrop of the beautiful castle with 100,000 people together for one reason - to have a good time and to celebrate the New Year."
Edinburgh's Prince's Street was packed with revellers for the celebrations
Lothian and Borders Police said the festivities in the capital had been safe and successful with only three arrests, for breach of the peace.
Assistant Chief Constable Bill Skelly said: "We have been delighted with the behaviour and attitude of revellers in Edinburgh this Hogmanay.
"We would like to thank the public for ensuring Edinburgh welcomed in the New Year in a fun but safe environment."
Singers Amy Macdonald and Sandi Thom headed Aberdeen's party at Castlegate, while The Magic Numbers had top billing in Inverness.
In the seaside town of Stonehaven, crowds were treated to a spectacular fireball parade, while Deacon Blue played at Stirling Castle Esplanade.
In Oban, cult bagpipe group the Red Hot Chilli Pipers were performing.
Despite the low temperatures, the calm weather conditions dispelled fears of a repeat of 2006 when high winds and torrential rain forced the cancellation of events in Edinburgh, Glasgow and Stirling.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.