The Prime Ministers video message saw her pile pressure on politicians to support her Withdrawal Agreement when it is put before the Commons.
She said while the 2016 referendum was "divisive" there was a chance to make 2019 "the year we put our differences aside and move forward together".
In her video message, she said: "New Year is a time to look ahead and in 2019 the UK will start a new chapter.
"The Brexit deal I have negotiated delivers on the vote of the British people and in the next few weeks MPs will have an important decision to make.
"If Parliament backs a deal, Britain can turn a corner."
“Together, I believe we can start a new chapter with optimism and hope.”
MPs return to Parliament next week, with debate on the Brexit deal due to start on January 9 before a meaningful vote the following week.
Mrs May also used the message to attempt to look beyond Brexit, saying settling the deal would allow time and energy to be spent on areas like housing, trade, the NHS, immigration reform and the environment.
Highlighting the Government's 2018 achievements, she added: "Together, I believe we can start a new chapter with optimism and hope.
"We have all we need to thrive and if we come together in 2019 I know we can make a success of what lies ahead and build a country that truly works for every one of us."
PRIME MINISTER: Theresa May used her New Year message to plea for unity over Brexit (Pic: PA)
Mrs May has endured a bruising year in Westminster which saw open rebellion against her leadership from within the Tories – including resignation of two Brexit secretaries, Dominic Raab and David Davies.
She survived a crucial vote of no-confidence against her led by Tory rebels furious with her Brexit plans, slamming them as a betrayal of the what Britain voted for in the EU Referendum.
The Prime Minister has been adamant her plan is the only way to go forward unless Britain risks crashing out with “no deal” on March 29.
It is expected May will now step aside and not lead the Tories into the next General Election – which will have to occur before May 5, 2022.
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PLEA: Vince Cable has urged Britain it has '90 days to change the course of this country' (Pic: PA)
Jeremy Corbyn used his New Year message to accuse Theresa May's Government of plunging the country into crisis by making a "mess" of Brexit.
The Labour leader said the Prime Minister's efforts to force through her Withdrawal Agreement in a crunch Commons vote next month were "letting people down all across the country, whether they voted Leave or Remain".
In the message, released on social media on Monday morning, he said the UK was full of talent that was being held back by the economic system and Conservative rule.
BRITAIN: The UK voted to Leave by a margin of 52 to 48 back in 2016 (Pic: GETTY)
Liberal Democrat leader Sir Vince Cable has said in his New Year message that the UK enters 2019 with "90 days to change the course of this country".
Sir Vince said the next three months will be "critical" to the future of the UK, and insisted it is still possible for the battle to stop Brexit to be won.
He urged opponents of EU withdrawal to "keep fighting" for a second referendum, which he described as "the only way forward" following Theresa May's poorly-received deal with Brussels.
And he accused the Prime Minister of trying to "frighten" MPs into backing her Withdrawal Agreement in next month's crunch Commons vote with warnings of serious disruption to travel and business.