She has already announced her intention to trigger Article 50, the formal mechanism for leaving the EU, by the end of March.
And she insisted this would be the year Brexit began and a “truly united” Britain would emerge.
Mrs May said: “The New Year is a time to reflect on what has passed and to look ahead to the opportunities to come. And this year, as I consider all that 2017 has in store, I believe those opportunities are greater than ever.
“For we have made a momentous decision and set ourselves on a new direction. And if 2016 was the year you voted for that change, this is the year we start to make it happen.
Mrs May said that she will work to achieve the ‘right deal’ when leaving the EU
If 2016 was the year you voted for that change, this is the year we start to make it happen
“But I know too that, as we face the opportunities ahead of us, our shared interests and ambitions can bring us together.
“We all want to see a Britain that is stronger than it is today. We all want a country that is fairer so that everyone has the chance to succeed.
“We all want a nation that is safe and secure for our children and grandchildren.
“So when I sit around the negotiating table in Europe this year, it will be with that in mind – the knowledge that I am there to get the right deal – not just for those who voted to Leave – but for every single person in this country.”
Styling herself as a major social reformer, the Prime Minister planted herself firmly in the centre ground of politics.
She declared: “This is the year we need to pull down the barriers that hold people back, securing a better deal at home for ordinary, working people.
The union between Scotland, England, Wales and N. Ireland is key to Mrs May’s vision of Britain
“After all, it is through unity that our people have achieved great things, through our precious union of nations – England, Scotland, Wales and Northern Ireland – and through our union of people, from sports teams to armed forces, businesses to charities, schools to hospitals, and above all through our union of communities and families.
“Of course, it isn’t just global events that define a year – it is the personal things. 2017 might be the year you start your first job or buy your first home.
“It might be the year your children start school or go off to university, or that you retire after a lifetime of hard work. These things, life’s milestones, are things that bind us, whoever we are.”
Mrs May paid homage to murdered MP Jo Cox and pledged to fix divisions caused by Brexit
“We have a golden opportunity to demonstrate that, to bring this country together as never before, so that whoever you are, wherever you live, our politics, economy and society work for you, not just a privileged few.
“So as we look ahead to a year of opportunity and unity, let me wish you and your family a peaceful, prosperous and happy New Year.”
He said the UK now had “the chance to do things differently” after the vote. He also said Labour would not block Brexit but would not support a deal with the EU which merely “protects the bankers in the City”.
Ukip leader Paul Nuttall urged the Government to use the “momentous” referendum result to boost global trade links and deliver a “real Brexit”.
“That is a Brexit whereby we control our own borders, it’s a Brexit whereby we make the legislation at Westminster, it’s a Brexit whereby we don’t pay a membership fee into the European Union,” he said.
Jeremy Corbyn’s New Year message said that Brexit was a chance for the UK to ‘do things differently’
The Archbishop of Canterbury Rev Justin Welby was criticised by the former Ukip leader Nigel Farage for not mentioning Brexit in his Christmas Day sermon.
But the 60-year old will say in his New Year’s address – broadcast today on BBC One at 1.50pm – that the vote will “profoundly affect the future of our country”.
Archbishop Justin Welby’s message also touched on healing the divisions caused by Brexit
“But I know that if we look at our roots, our history and our culture in the Christian tradition, if we reach back into what is best in this country, we will find a path towards reconciling the differences that have divided us.
“If we are welcoming to those in need, if we are generous in giving, if we take hold of our new future with determination and courage – then we will flourish.”