"New Year is a time to look ahead and in 2019 the UK will start a new chapter," May said, as Britain prepares to leave the European Union on March 29.
"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."
Most British lawmakers do not back the deal May reached with the European Union.
They are due to debate the UK-EU withdrawal agreement on Wednesday next week, before voting the following week.
The 2016 referendum on leaving the EU, was "divisive", the prime minister said, "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."
Once Britain left the EU, the Conservative government could focus its energy on boosting the economy, opening up new markets, and building homes, she added, while a skills-based immigration system would replace the free movement of EU migrants.
"Together I believe we can start a new chapter with optimism and hope," May said.
A spokeswoman for May's Downing Street office said discussions between London and Brussels had continued, and the prime minister was working on getting "legal and political assurances".
May had "been in contact with European leaders and that will continue in the lead up to the vote", the spokeswoman added.
"Her focus is certainly on getting the assurances that MPs want ahead of that vote taking place. There is still work to do and talks will continue."
In a message posted on Twitter, Jeremy Corbyn, leader of the opposition Labour Party, denounced the Conservative Party's handling of Brexit as "a complete mess".
"Eight years of damaging Tory failure has left us with a divided country where millions are struggling to make ends meet," he said.