Tony Blair has called on the government to introduce a new UK immigration policy which "reasserts control".
He wants tougher immigration rules for EU citizens.
When he was prime minister, his government - unlike most EU countries - did not apply transitional controls on migrants from eastern Europe.
But in a Sunday Times article, he said "times were different" now, and all EU nationals should register on arrival and should already have a job offer.
However, Mr Blair still opposes leaving the EU, saying it will be "painful".
He says tougher immigration policies could "deal with the anxieties" that he says led to the Brexit vote - without the UK necessarily having to go through with it.
Under existing rules, citizens of other EU countries can be removed after six months if they have not found a job, have no realistic possibility of finding one, and require support from the welfare system.
But the new report by Mr Blair's Institute for Global Change says EU nationals should already have an offer of work when they arrive.
Those who didn't earn permission to stay would be banned from opening a bank account, renting a home or claiming benefits.
The report also proposes restricting free healthcare for unemployed migrants and letting universities charge EU nationals higher tuition fees than British students.
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He argues his approach "reaches out to Leave voters to show their concerns are better met", without "the damage" he claims Brexit will do.
And he acknowledges that his thinking has changed.
"My government in 2004 did not invoke the transitional arrangements when eastern Europe joined the EU," he writes.
"Back then the economy was strong, the workers were needed and actually the biggest annual numbers came post-2011.
"But the real point is that the times were different; the sentiment was different; and intelligent politics takes account of such change."
The co-chairman of the campaign group Leave Means Leave, Richard Tice, said Tony Blair's attempt to deny democracy would be seen for what it was.
Downing Street declined to comment.