In her statement to the House of Commons, May said that the draft deal that Britain agreed with the EU, which is good for both sides, "ends free movement once and for all."
Britain and the European Union agreed in principle to a text setting out their future relationship before a summit on Sunday, according to media reports.
The euro and British pound jumped following the news, which put the US dollar under pressure.
The dollar index, which measures the greenback against six major peers, fell 0.23 per cent at 96.4872 in late trading.
--IANS pgh/