"During the implementation period, people will be continue to be able to come and live and work in the UK but there will be a registration system, an essential preparation for the new regime," May said in Florence.
"As of today, these considerations point to a implementation period of around two years," she said.
Other highlights from the speech included:
MAY ON IMPLEMENTATION PERIOD FOR NEW RELATIONSHIP WITH EU
"During the implementation period, people will continue to be able to come and live and work in the UK but there will be a registration system, an essential preparation for the new regime. As of today, these considerations point to an implementation period of around two years."
"Clearly people, businesses and public services should only have to plan for one set of changes in the relationship between the UK and the EU. So during the implementation period, access to one another’s markets should continue on current terms and Britain also should continue to take part in existing security measures. And I know businesses, in particular, would welcome the certainty this would provide."
MAY, ASKED WHETHER SHE STILL THINKS NO DEAL ON BREXIT WOULD BE BETTER THAN A BAD DEAL:
"We continue to think that."
MAY, ON HOW LONG BREXIT NEGOTIATIONS MIGHT RUN
"Of course we will leave at the end of March 2019 and negotiations will be continuing potentially up quite close to that time."
MAY ON EU BUDGET
"I do not want our partners to fear that they will need to pay more or receive less over the remainder of the current budget plan as a result of our decision to leave. The UK will honour commitments we have made during the period of our membership.
"And, as we move forwards, we will also want to continue working together in ways that promote the long-term economic development of our continent. This includes continuing to take part in those specific policies and programmes which are greatly to the UK and the EU's joint advantage, such as those that promote science, education and culture - and those that promote our mutual security."
MAY ON UK COURTS REFERRING TO EUROPEAN COURT OF JUSTICE
"Over time ... the rights of EU citizens in the UK, and UK citizens overseas will diverge. And I want to incorporate our agreement fully into UK law, and make sure the UK courts can refer directly to it. And when there is uncertainty around underlying EU law, I want the UK courts to be able to take into account the judgements of the European Court of Justice with a view to ensuring consistent interpretation. And on this basis I hope our teams can reach firm agreement quickly."
MAY ON UK NOT FEELING AT HOME IN EU
"Throughout its membership, the United Kingdom has never totally felt at home being in the European Union.
"And, perhaps because of our history and geography, the European Union never felt to us like an integral part of our national story, in the way it does to so many elsewhere in Europe. It is a matter of choices.
"The profound pooling of sovereignty that is a crucial feature of the European Union permits unprecedentedly deep cooperation which brings benefits but it also means that when countries are in the minority they must sometimes accept decisions they do not want, even affecting domestic matters with no market implications beyond their borders."
MAY ON OPTIMISM
"We are moving through a new and critical period in the history of the United Kingdom's relationship with the European Union. The British people have decided to leave the EU and be a global free-trading nation able to chart our own way in the world.
"For many, this is an exciting time full of promise. For others it is a worrying one. I look ahead with optimism."
MAY ON WORKING WITH EU ON DEFENCE, SECURITY
"Our commitment to the defence and indeed the advance of our shared values is undimmed. Our determination to defend the stability, security and prosperity of our European neighbours and friends remains steadfast."
MAY ON PROGRESS SO FAR IN BREXIT TALKS
"We have now conducted three rounds of negotiations and while at times those negotiations have been tough it's clear that, thanks to the professionalism and diligence of David Davis and Michel Barnier, we have made concrete progress on many important issues."
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