Blair, who led the Labour Party from 1994 to 2007, will not be standing in the June 8 general election.
But he said he wanted to build a political movement to shape the policy debate as Britain starts its negotiations to leave the European Union.
Blair, 63, who was prime minister for a decade from 1997 and whose legacy has been defined by the Iraq war, said he knew he would face intense criticism for doing so.
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But the ardent Europhile, who has largely been working on Middle East and African issues since leaving office, still wanted to get his "hands dirty" and re-enter the fray, saying voters should have the chance to change their mind once the final EU exit deal becomes clear.
"This Brexit thing has given me a direct motivation to get more involved in the politics," he told the Daily Mirror newspaper.
"You need to get your hands dirty and I will.
"I know the moment I stick my head out the door I'll get a bucket of wotsit poured all over me, but I really do feel passionate about this.
"I don't want to be in the situation where we pass through this moment of history and I hadn't said anything because that would mean I didn't care about this country. I do.
"I am not sure I can turn something into a political movement but I think there is a body of ideas out there people would support."
He said his push was not about defying the vote to leave the European Union.
He said leaving the European single market and seeking a free trade agreement, as is Conservative Prime Minister Theresa May's intention, would be "relegating ourselves" from the top order.
Opinion polls put the Conservatives far ahead of Labour, a few weeks out from the general election.
Blair, who won three straight general elections as Labour leader, was from the most centrist strain of the party, while current leader Jeremy Corbyn is from its strident leftist wing that reviles Blairite politics.
"Unless you are providing answers for the future you are not going to win," Blair warned.
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