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He urged the party he once led to "nail" the "myths" of the Brexit campaign - and fight for the rights of voters to "think again" about leaving.
He said 2018 would be the year the fate of Britain would be decided.
Labour has backed Brexit and ruled out a second referendum if it wins power.
Britain is due to leave the EU on 29 March 2019, but Mr Blair said it would be too late to change course by then.
Shadow Brexit Secretary Sir Keir Starmer says Labour will push for a deal that would preserve as many of the benefits of the single market and customs union as possible, as well as protecting workers' rights and the environment.
But Mr Blair believes this is a "confusing" strategy and is not "credible".
"Far better to fight for the right for the country to re-think, demand that we know the full details of the new relationship before we quit the old one, go to the high ground on opposing Brexit and go after the Tories for their failures to tackle the country's real challenges.
"Make Brexit the Tory Brexit. Make them own it 100%. Show people why Brexit isn't and never was the answer."
Mr Blair - a longstanding critic of Labour leader Jeremy Corbyn - has ditched his business interests to take a more active role in British politics through his Institute for Global Change think tank.
He has previously attacked Mr Corbyn's stance on Brexit - prompting the Labour leader to say Mr Blair should respect the result of the 2016 EU referendum.
Richard Tice, co-chairman of the group Leave Means Leave, said Mr Blair "and his elite gang" were "still determined to stop Brexit" and will lead the UK "to the very bad deal which we had in the single market and the customs union".
"We will thrive and prosper by leaving both and regaining our rightful place on the global stage as a strong powerful independent nation and the sooner the better," he said.
In Mr Blair's latest article, which will be published on the institute's website, he said Labour should take "the high ground on opposing Brexit and go after the Tories for their failures to tackle the country's real challenges".
"At every PMQs nail each myth of the Brexit campaign, say why the Tory divisions are weakening our country, something only credible if we are opposed to Brexit, not advocating a different Brexit, and challenge the whole farce head on of a prime minister leading our nation in a direction which even today she can't bring herself to say she would vote for.
"If we do leave Europe, the governing mind will have been that of the Tory right.
"But, if Labour continues to go along with Brexit and insists on leaving the single market, the handmaiden of Brexit will have been the timidity of Labour."