Britain's departure from the bloc, completed in December, ended the freedom of movement for Britons and EU citizens in each other's countries.
Johnson, who was a figurehead of the successful campaign for Britain's departure from the European Union, said over 5.6 million EU citizens had applied for the government's settlement scheme and urged others to do so before the deadline on June 30.
In the June 23, 2016, referendum, 17.4 million voters, or 52%, backed Brexit while 16.1 million, or 48%, backed staying in the bloc.
England and Wales voted out but Scotland and Northern Ireland voted in.
The referendum revealed a United Kingdom polarized about much more than the European Union, and fuelled soul searching about everything from secession and immigration to capitalism, the legacy of empire, and what it now means to be British.