Prime Minister David Cameron will apply for an emergency debate in the House of Commons today on the proposals for reforming press regulation, the Speaker's Office said.
Conservatives had earlier given ground on two key principles in reaching cross-party agreement on the future of press regulation.
A revised version of the proposed royal charter to govern the regulation of the press will not give the industry a veto over the membership of a new watchdog body, and will give the regulator the power to "direct" newspapers on the size and positioning of apologies, Prime Minister David Cameron's official spokesman said.
Mr Cameron will set out the details of the cross-party deal, struck in the small hours of the morning after negotiations stretched late into the night, in a statement to the House of Commons later.
The Prime Minister insisted the agreement avoids the need for a law to control newspapers, telling reporters: "It's not statutory underpinning. What it is is simply a clause that says politicians can't fiddle with this so it takes it further away from politicians, which is actually, I think, a sensible step."
But his comment appeared to be at odds with the view of the new arrangements taken by Labour and Liberal Democrats, who had threatened to combine to defeat Mr Cameron in the Commons this evening if a cross-party deal was not reached.
A senior Labour source suggested Conservatives were trying to save face, insisting: "This is not a little bit of statute, this is not a dab of statute, this is statute pure and simple."
And Liberal Democrat leader Nick Clegg said the plan achieved what he had hoped for when he published joint proposals with Labour's Ed Miliband last Friday.
"In effect what we have done is adopt the so-called 'royal charter plus' in full, which we published last Friday and it is underpinned by legislation - both to install a real system of costs and damages and crucially to make sure that future governments can't mess around with the Royal Charter in a way that everyone had concerns (about)," said the Deputy Prime Minister.
Meanwhile, press reform campaigners Hacked Off have welcomed the cross-party deal struck to bring in new regulation of the industry saying they believed it "can effectively deliver" Lord Justice Leveson's recommendations.