But Hammond told BBC radio that EU nationals would have to register with the authorities starting from the expected departure date of March 2019 as the government comes up with a new immigration system.
"Many things will look similar" and goods will continue to flow between Britain and the EU in "much the same way as they do now" even after the scheduled departure date of March 2019, he said.
Hammond, who campaigned for Britain to stay in the EU in last year's referendum but now supports withdrawal, is seen as an advocate of a more moderate "soft Brexit" in contrast to more hardline ministers.
According to the Financial Times newspaper, Hammond unveiled the plan to business leaders earlier this week, arguing there was not enough time to negotiate a "bespoke" deal before the March 2019 deadline.
"He told us the Europeans now agree a cliff edge would harm both parties," a person present at the meeting told the FT.
More than a decade of mass immigration from the bloc under freedom of movement rules was a major factor in the June 2016 referendum that saw Britons vote to leave the EU.
Prime Minister Theresa May has so far insisted that Brexit needs tougher immigration rules, including an end to free movement of EU citizens.
According to Hammond, "Europeans will still be able to come into the UK" during the transition period, "but they will have to register with the authorities so we know who's coming and who's going".
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