The UK can "turn a corner" and start to "put its differences aside" if Parliament backs the proposed Brexit deal, Theresa May has said.
In her new year message, the prime minister said 2019 would mark a new chapter for the country outside the EU.
Should MPs approve the exit terms later this month, she said the UK could "move forward together" and concentrate on other issues like housing and health.
Labour has said the Brexit process is a "complete mess" due to Tory divisions.
The UK is scheduled to leave the union on 29 March, but it is unclear what will happen if MPs reject the withdrawal agreement and the framework for future relations.
MPs are due to vote in the Commons in mid-January on the proposals reached with the EU.
Downing Street has said there is "still work to do" - as the PM seeks to persuade sceptical Conservative MPs, some of whom believe the agreement does not represent the Brexit the country voted for in 2016.
The prime minister is continuing to seek further assurances from European leaders about aspects of the agreement, notably the controversial Irish border "backstop", designed to prevent physical customs checks on the island of Ireland.
No 10 said the prime minister had been in contact with European counterparts during the Christmas break and that would continue in the coming week.
In her message, Mrs May said MPs had an "important decision to make".
"In 2019 the UK will start a new chapter. The Brexit deal I have negotiated delivers on the vote of the British people. If Parliament backs a deal, Britain can turn a corner.
"The referendum in 2016 was divisive. But we all want the best for our country and 2019 can be the year we put our differences aside and move forward together, into a strong new relationship with our European neighbours and out into the world as a globally trading nation."
An orderly Brexit, she argued, would enable the UK to "focus its energy" on other challenges, such as addressing housing shortages, improving technical education and ensuring the £20bn in extra spending planned for the NHS during the next five years ensures the health service continues to be "there for us when we need it".
With employment at a record high and debt falling, the PM said the UK's economic foundations were strong but she acknowledged more needed to be done to ensure "everyone in every community can feel the benefit".
What is Jeremy Corbyn saying?
Labour has warned uncertainty over Brexit has plunged the country into a state of crisis and the agreement on the table would not satisfy either Leave or Remain voters.
The opposition is seeking to force a general election by calling a vote of no confidence in the government if the deal is rejected by MPs. However, Jeremy Corbyn has insisted that the decision to leave the EU cannot be reversed.
In his new year message, Mr Corbyn said Mrs May could not be allowed to "drive through a bad deal" and Labour, if it was in power, would seek to reopen negotiations with Brussels to pursue a better outcome.
Only his party, he claimed, was capable of uniting the UK, with policies to tackle inequality and job insecurity.
"Eight years of damaging Tory failure has left us with a divided country where millions are struggling to make ends meet," he said. "We cannot go on like this.
"Labour is ready to deliver a radical alternative to rebuild and transform our country. We will stand up to the powerful few so the wealth you create is shared fairly, not hoarded by a privileged elite.
"We will work to create a society where the talent of everyone is unleashed. That is how we will unite our country."
And other party leaders?
Liberal Democrat leader Sir Vince Cable insisted Brexit can be stopped as he urged fellow supporters of another referendum on the UK's future in Europe to "keep fighting".
As we enter 2019, time is ticking down on Brexit, and with it the whole future of the country.— Vince Cable (@vincecable) December 31, 2018
The history books will look back on the coming three months as critical.
Let's get out there in 2019 and win the fight for a People's Vote and a brighter future for Britain. pic.twitter.com/dB4QSTeD3r
"Are we going to make a terrible mistake, leaving behind our influence in Europe's most successful peace project and the world's biggest marketplace?" he said.
"Or are the British people, in the final hours, going to be given a chance to reconsider, in light of all the facts which have come to the surface in the last two years?"
Meanwhile, Scottish First minister Nicola Sturgeon has sought to assure EU nationals living in Scotland that they were "hugely valued", despite the current uncertainty about their future status.
"Our reputation for being an open, warm-hearted, hospitable country has never been more important," the SNP leader said in her Hogmanay message.
"I want to make that especially clear to the hundreds of thousands of nationals from other EU countries, who have done us the honour of choosing Scotland as their home."
Plaid Cymru leader Adam Price said Wales needed to make its voice heard and the Welsh people given a "real choice" about their future in Europe.