The Prime Minister will promise an in-out referendum by November 2017, should the Conservatives win the 2015 General Election, saying that public disillusionment with the EU is now at an all-time high and democratic consent is "wafer thin".
"It is time for the British people to have their say; it is time to settle this European question in British politics," he will declare.
Mr Cameron will be hoping his "red meat" speech on Europe will be enough to satisfy the bulk of Conservative Eurosceptics and neutralise the threat from the anti-EU UKIP.
However, it will open up a new front with the SNP, arguing that the only guarantee of Scotland staying in the EU is for Scots to vote for independence.
His eagerly awaited speech in the City this morning comes within hours of Downing Street – faced with borrowing up £7 billion on the same period last year, a fall in manufacturing export orders and the announcement by Rolls-Royce of 400 job losses at its plant near Coventry – insisting the UK economy is "healing".
In it, the PM will argue that, with "courage and conviction", a better, more flexible EU can be created, one with which Britain is comfortable.
He will set out his vision for Europe based on five principles: competitiveness; flexibility; power flowing back to, not just away from, member states; democratic accountability; and fairness.
Mr Cameron will claim that Labour, the Liberal Democrats and Europhile Tories like Lord Heseltine, who argue against holding an in-out referendum, would make Britain's eventual exit more likely.
"Simply asking the British people to carry on accepting a European settlement over which they have had little choice is a path to ensuring that when the question is finally put – and at some stage it will have to be – it is much more likely that the British people will reject the EU.
"That is why I am in favour of a referendum. I believe in confronting this issue, shaping it, leading the debate, not simply hoping a difficult situation will go away."
The PM will say he understands the "impatience" of those, including many on the Tory backbenches, who want a referendum now, but will insist this would present a false choice between the status quo and leaving the EU.
It would be wrong to ask people whether to stay or go before there is a chance to put the relationship right. "How," he will ask, "can we sensibly answer the question 'in or out' without being able to answer the most basic question: 'what is it exactly that we are choosing to be in or out of'?"
Mr Cameron will argue that the EU that emerges from the eurozone crisis could be transformed beyond recognition and that time will be needed to enable a real choice to be offered.
The PM will explain that the Tories' next election manifesto will ask voters for a mandate to negotiate a new settlement with fellow member states in the next Parliament.
"When we have negotiated that new settlement, we will give the British people a referendum with a very simple in-or-out choice to stay in the EU on these new terms or come out altogether. It will be an in-out referendum."
Legislation will be drafted before the election, which, if the Tories win, will be introduced immediately and passed by the end of 2015. Negotiations with Brussels will be completed and the referendum itself held "within the first half of the next Parliament", ie by November 2017.
In extracts already released ahead of his postponed speech in Amsterdam last week, the PM said that if the EU did not meet the challenges of sorting out the eurozone crisis, increasing competitiveness and tackling a lack of public support, Britain would "drift towards the exit".
Today, he will add: "I believe something very deeply: that Britain's national interest is best served in a flexible, adaptable and open European Union; and that such a European Union is best with Britain in it."
Ahead of the speech, Ed Miliband insisted it would define Mr Cameron as "a weak Prime Minister, being driven by his party, not by the national economic interest".
The Labour leader insisted the priority for Britain was growth and jobs.
He added: "This speech will do nothing for a young person looking for work, for a small business worried about a loan, for the family whose living standards are squeezed. Britain needs a Prime Minister who is making change happen now in Europe, ensuring that we put jobs and growth ahead of austerity and unemployment."