The Labour leader, under whose leadership the UK is seen as having opened its doors to migration from around the world in the 1990s, said the times have changed.
Writing in 'The Sunday Times', Blair acknowledged that he has changed his mind since his government had chosen not to invoke transitional controls on migrants from newer EU members from eastern Europe, unlike most other countries within the union.
He writes: "My government in 2004 did not invoke the transitional arrangements when eastern Europe joined the EU. Back then the economy was strong, the workers were needed and actually the biggest annual numbers came post-2011.
Blair's Institute for Global Change has released a report that says EU nationals should already have an offer of work when they arrive in the UK.
Those who didn't earn permission to stay would be banned from opening a bank account, renting a home or claiming benefits.
Under existing rules, citizens of other EU countries can be removed after six monthsif they have not found a job, have no realistic possibility of finding one, and require support from the UK's welfare system.
Blair says the concerns of "leave" voters about "pressure on services", "downward pressure on wages", the "cultural integration" of migrants and control now "cannot be ignored".
He warns opponents of Brexit that they must accept "uncomfortable choices".
"There is no diversion possible from Brexit without addressing the grievances which gave rise to it. Paradoxically, we have to respect the referendum vote to change it," Blair writes.
His institute's report, authored by Harvey Redgrave, a former Downing Street policy expert, suggests British Prime Minister Theresa May seeks to get the EU to modify its freedom of movement rules by introducing an emergency brake on new arrivals when public services are overstretched.
He writes: "We can curtail the things that people feel are damaging about European immigration, both by domestic policy change and by agreeing change within Europe. This is precisely the territory the Labour Party should camp upon.
"If we go ahead with Brexit, we will have taken the unprecedented decision for a major country to relegate ourselves, like a top-six Premiership side deciding to play exclusively in the Championship.
Downing Street has chosen not to comment on the report's findings or Blair's intervention so far.
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