The former Labour PM issued a strong call for Remainers to fight for Britain to remain in the EU in a speech on Friday – despite last year's vote to quit the EU.
Mr Blair, who has made millions since leaving office in 2007, told an audience in central London that Brexiteers acted with "imperfect knowledge" when they voted Leave.
Mr Duncan Smith, who was Mr Blair's direct rival during his time as Tory leader, was savage as he criticised the ex-PM for his globe-trotting consultancy work.
He told Sky News: "The idea we are going to have Tony Blair coming in, late in the day lecturing, after advising quasi-dictators around the world what to do.
"He seems to have forgotten what democracy is about.
Iain Duncan Smith attacked Tony Blair over his inflammatory speech
The people voted that they want to leave it and now the job of the government is to get along and do that
Iain Duncan Smith
“Democracy is about asking people a question and then acting on it. That’s what we did and that’s what we are doing at the moment. The government and Theresa May is doing exactly the right thing.
“The idea that you just keep on asking the British people until they give you the right answer to the question, which is his case, and some of his political elite friends is no we don’t want to leave the European Union is arrogant really.”
The former Work and Pensions secretary denied that people were misinformed during the debate and said that his Government was working to deliver Brexit.
Mr Duncan Smith said: “The British people made a decision only a matter of months ago after a robust and fairly long debate, asked the question, do you want to stay or do you want to leave the European Union.”
Blair and Juncker: Together through the years
Wed, January 25, 2017
Former Prime Minister, Tony Blair and President of the European Commission, Jean-Claude Juncker have always shared a friendly relationship over the years.
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EU Commission President Juncker greets former British PM Blair in Brussels
“The people voted that they want to leave it and now the job of the government is to get along and do that.”
Mr Blair delivered his speech at Bloomberg HQ on Friday and set out what he believes is a path to push for Britain to remain in the EU.
He said: “What was unfortunately only dim in our sight before the referendum is now in plain sight.
"The road we're going down is not simply ‘hard Brexit’. It is Brexit at any cost.
“Our challenge is to expose relentlessly what this cost is, to show how the decision was based on imperfect knowledge which will now become informed knowledge.”