Freedom of movement of people between Britain and the European Union will end when Britain withdraws from the bloc, immigration minister Brandon Lewis has said.
"Free movement of labour ends when we leave the European Union in spring 2019," Mr Lewis told BBC radio.
Mr Lewis also said a new immigration system would be in place by spring 2019.
Britain is due to leave the EU in March 2019.
In an article in the Financial Times, Interior Minister Amber Rudd said: "Once we have left the EU, this government will apply its own immigration rules and requirements that will meet the needs of UK businesses, but also of wider society.
"I also want to reassure businesses and EU nationals that we will ensure there is no 'cliff edge' once we leave the bloc," Ms Rudd added.
Meanwhile, Brexit Secretary David Davis is confident EU withdrawal negotiations will continue as planned after reports that Brussels may delay trade talks because of a lack of progress on the financial "divorce" settlement.
The upbeat government assessment followed a report in the Daily Telegraph which said the EU's chief negotiator, Michel Barnier, had told a private meeting of ambassadors that the next phase of negotiations would be delayed by two months because of the wrangle over how much the UK owes the bloc.
The report stated that Mr Barnier said the EU would not talk about trade or the UK's future relationship with Brussels until "sufficient progress" had been made on the exit payment, citizens' rights and the Northern Ireland border issue.
The EU had planned to assess whether the negotiations could move on to post-Brexit trade relations in October, but this could now slip back to December, the newspaper said.
However, the Department for Exiting the EU said the government expected the next stage to begin in October as planned.
A spokesman said: "Negotiations to leave the EU are under way and we have already made good progress on a number of issues.
"As the secretary of state said, it is important that both sides demonstrate a dynamic and flexible approach to these negotiations.
"Government officials are working at pace and we are confident we will have made sufficient progress by October to advance the talks to the next phase.
"On the financial settlement, we have been clear that we recognise the UK has obligations to the EU and that the EU also has obligations to the UK."
European Commission spokeswoman Mina Andreeva would not be drawn on what was said at the meeting with ambassadors.
At a press briefing in Brussels she said Mr Barnier had publicly acknowledged that "so far limited progress has been achieved in the negotiations" but EU officials were ready to work on the issues over the summer if the UK side provided further updates.
She said European Commission president Jean-Claude Juncker was committed to engaging with the UK.
"President Juncker has asked, specifically, the task force on Article 50 to be ready every day throughout the coming weeks, throughout the month of August, to engage with our British counterparts should the UK wish to substantiate their position in some of the cases where it has not happened yet," she said.
"The commission stands ready, we are ready to work and I cannot, beyond that, speculate on any timetable because that will depend on the pace of the progress being made."
