He said: "Theresa understands that if you want to take control you have to command the high ground. She will be giving clarity by setting a clear deadline while the European Union looks increasingly muddled and mean-spirited".
The announcement means that the "cut-off date" for EU migrants is likely to be around March 15, once the Government's Article 50 bill has gone through Parliament.
The Prime Minister is expected to appeal to other European Union nations to reach a quick deal on the issue so it can be removed from Brexit negotiations as soon as possible.
It is likely to put her in conflict with the European Union, which has been pushing for Mrs May to delay the cut-off date until 2019. However ministers have raised concerns that waiting until the end of negotiations will lead to a huge surge in the number of EU migrants coming to the UK before Brexit.
"We have had some suggestion that that the European Commission might attempt to force us to protect everyone who arrives up to the moment of departure," a Government source said. "We could end up with half of Romania and Bulgaria coming here if we wait that long."
The Government has also considered suggestions that the cut-off date should be set for the referendum date in June last year. However Government lawyers have advised that such an approach would be illegal.
Amber Rudd, the Home Secretary, said that after Britain leaves the European Union "we will be ending free movement as we know it".
She is examining plans to give new arrivals who get jobs in key sectors of the economy multi-year visas while limiting access to benefits.
Under one plan being considered migrants would be given five-year working visas but barred from claiming in-work benefits while they are in Britain.
She confirmed that the Home Office is "working on a range of options" but suggested that the final system will only be decided after "two years of negotiations and preparation".
David Davis, the Secretary of State for Leaving the European Union, has previously suggested that Britain will not suddenly shut the door on workers coming from the EU.
He suggested that it will take "years and years" for Britain to fill all the jobs that would otherwise have been done by EU migrants.
Asked about his comments Mrs Rudd said that the Government does not want a "cliff-edge", suggesting that migration controls could be limited initially after Brexit.
She said: "I think what he [David Davis] is highlighting is the fact that as a government we're going to work with businesses, with employers to make sure that the immigration system we put in place does enable them to continue to thrive and continue to grow. What shape that will be we can't say yet.
"We are against cliff edges. So as part of the consultation that we will be bringing out in the summer we will be asking them the best way to deliver that."
While the UK has reached agreements in principle with most members of the European Union already there are still several nations, including Germany, who have refused to discuss the issue until after Brexit is triggered.
Mrs May is also facing a rebellion in the House of Lords over the issue where Tory peers are prepared to back a campaign by Labour and the Liberal Democrats to guarantee the rights of EU nationals.
It came after reports that ministers are also discussing plans to give the independent Migration Advisory Committee (MAC) an advisory role on how many visas should be issued to take the political sting out of the issue.
The committee would decide how many visas need to be issued for workers in key industries such as software engineering, health and social care, farming and hospitality, which are heavily reliant on immigrants.
The cut-off date for the 1.2million British nationals living in other EU countries will ultimately be decided by Brussels. The European Parliament's chief negotiator has suggested that the EU will offer British people to individually opt-in and remain European citizens.
