The show culminated at 8.13pm on Monday (20:13) and took place against the backdrop of St Columb's Park, River Foyle and the Peace Bridge.
It included visual electric performance from Lords of Lighting along Queen's Quay, a boat arriving with light and flares with an individual carrying a "Flame of Hope" which subsequently crossed the Peace Bridge from the city to Ebrington.
Earlier church bells across the city rang out calling people to join in the celebrations at the start of a year-long programme of arts.
Members of the public got involved by leaving wishes for the New Year for a virtual wall that will be part of the celebrations in 2013.
Musical entertainment was also provided across a number of venues.
The show ended with the sounds of the Shirt Factory horns, which organisers said welcomed the New Year and "our ambitions for a brighter future for the city".
Derry is the first ever UK City of Culture, with over a million visitors expected and 140 events scheduled in 2013 - including the Turner Prize and the Royal Ballet's first visit to Northern Ireland for over two decades.
It is with great pride that I extend best wishes to everyone for 2013 and wish you all a very peaceful and prosperous year in 2013.
Mayor Kevin Campbell
There will also be a new commission by the London Symphony Orchestra, a new play by American playwright Sam Shepard, and the celebration of local Nobel Prize-winning poet Seamus Heaney.
The city will also host Fleadh Cheoil na hÉireann, the world's biggest festival of Irish culture with traditional music, bands and singing set to attract over 300,000 visitors.
Organiser Martin Bradley said: "As the first winners of this prestigious title, we have been pioneers, working without a blue print and setting benchmarks for future UK Cities of Culture."
"The journey to 2013 has undoubtedly been challenging, but rewarding and exhilarating."
Speaking ahead of the show, Culture Minister Ed Vaizey said: "2013 is shaping up to be a massively exciting year for Derry-Londonderry and for the UK as a whole. Their programme of events promises to be hugely entertaining and contains something for everyone.
"It will build on the phenomenal success of the London 2012 Cultural Olympiad, and show once again the depth and range of cultural excellence in this country."
Derry Mayor Kevin Campbell added: "The city celebrations marked a perfect moment to mark the arrival of 2013 and to look forward to what will be a fantastic cultural year for the city and region. It's our time to tell a new story and to showcase the best of local and international talent while marking the beginning of new opportunities for the city."