Freedom of movement, a facet of Britain's membership of the EU, will end as soon as Britain leaves the 27-member economic bloc - the deadline for which is March 2019, immigration minister Brandon Lewis said.
This would mean nationals of EU countries will face similar entry curbs as citizens of countries like India.
"Free movement of labour ends when we leave the European Union in the spring of 2019. I'll be very clear about that," Lewis told the BBC.
More than 3 million citizens of other EU countries live in Britain, and many sectors of the economy rely on foreign workers.
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Immigration was one of the key issues played up in last year's EU referendum campaign, with ministers promising to "take back control" of the UK's borders as they negotiate Brexit.
However, Lewis did not confirm details of how the government plans to manage migration after Brexit, saying these would be revealed in a white paper later this year, and that a new immigration bill would go through Parliament in 2018.
That report by the UK's Migration Advisory Committee is expected in September 2018, six months before Brexit.
"We will ensure we continue to attract those who benefit us economically, socially and culturally. But, at the same time, our new immigration system will give us control of the volume of people coming here - giving the public confidence we are applying our own rules on who we want to come to the UK and helping us to bring down net migration to sustainable levels," said UK home secretary Amber Rudd.
"There is far too much heat and not enough light about immigration, so any truly objective and well-informed analysis must be welcome," said Shadow home secretary Diane Abbott.
The Migration Advisory Committee's report will study the economic and social costs and benefits of EU migration to the UK economy, its impact on competitiveness, and whether there would be benefits to focusing migration on high-skilled jobs.
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