At an EU referendum event, the Leave campaigner advocated an amnesty for illegal immigrants who have been in Britain for 12 years.
Mr Johnson also called for an Australian-style immigration points system would enable Britain to "take back control" of its immigration policy.
The influx of migrants into Britain should be blamed on poor regulation of working conditions, not on migrants themselves, Jeremy Corbyn has said.
Speaking on BBC One's The Andrew Marr Show, the Labour leader said "endless" newspaper headlines have blamed everything on migration "without ever being prepared to look at the reality of the exploitation of people in this country and across Europe".
"Now there are several hundred people working on zero-hour contracts that have been shipped in from elsewhere," he said.
"The answer to that isn't to blame them. The answer is yes, on one level to blame Mike Ashley, but the other level is to blame the lack of regulation of working conditions both here and in other parts of Europe."
Mr Corbyn said the real issue is to improve working conditions and rights across Europe and target people making money out of exploitation.
In a 2013 interview, Boris Johnson says he wants Britain to be able to 'trade freely with our European friends'.
The Mail on Sunday and the Observer come out for remain while the Sunday Times and Sunday Telegraph back a Brexit.
David Cameron and George Osborne have issued an impassioned appeal for a vote for Remain, warning that Brexit would be the "big mistake"