The Prime Minister will say that leaving the EU is "not just a matter of jobs and trade but of the safety and security of our nation," The Telegraph reported.
The speech will kickstart the final stage of Cameron's attempts to reshape Britain's relationship with Brussels ahead of an in/out referendum on the UK's membership, the report says.
Cameron will also tomorrow to write a letter to Donald Tusk, the European Council President, setting out the areas of reform which Britain would like to see.
The letter is expected to make clear that the UK wants opt outs from ever closer union, more powers to block EU laws, no further interference in British trade and restrictions on benefits for EU migrants.
Read alsoStratfor's predictions in Business Insider: collapse of Russia, 4 Europes, 16 mini-Chinas next decadePhilip Hammond, the foreign secretary, warned yesterday that a proposal to stop paying benefits to EU migrants for four years could be illegal.
In his speech Cameron will say that the vote – which must be held within the next two years – will be "a huge decision for our country, perhaps the biggest we will make in our lifetimes."
He will tell voters: "You, the British people, will decide. At that moment, you will hold this country's destiny in your hands."
He will also formally rule out any chance of a second referendum after the in/out vote, as has been mooted by some Eurosceptics. The referendum will be "the final decision," he will say.
Cameron will make clear that he is "not saying for one moment that Britain couldn't survive outside the European Union – of course we could."
He will add: "No one doubts that Britain is a proud, successful thriving country. A nation that has turned round its fortunes though its own efforts.
"A far cry from the 'sick man of Europe' at the time we entered the European Economic Community four decades ago.
"Whether we could be successful outside the European Union is not the question. The question is whether we would be more successful in than out?
"Whether being in the European Union adds to our economic security or detracts from it? Whether being in the European Union makes us safer or less safe? That is a matter of judgment."
Read alsoTusk calls on German help on borders"We want to stay in, but not at any price and David Cameron is right to make that clear," Londom Mayor Boris Johnson wrote in his Telegraph column.
"One thing is sure: in the coming campaign we will hear absolute torrents of drivel from all the people who traditionally warn about us not being included in some European project big business, the CBI, the Europhiles in parliament.
"Remember: they were wrong about the ERM [European Exchange Rate Mechanism], they were wrong about the euro, and they are already exaggerating the exaggerating the downsides of leaving," Johnson said.
