European leaders say 26 out of 27 EU member states have backed a tax and budget pact to tackle the eurozone debt crisis.
Only the UK has said it will not join. Prime Minister David Cameron said he had to protect key British interests, including its financial markets.
The 17 countries that use the euro have all agreed to the deal.
Nine other countries have said they will sign up, some pending consultations with their parliaments.
Hungary originally said it would also remain outside the deal but has now changed its stance.
The UK effectively used its veto to block an attempt, led by the French and Germans, to get all 27 EU states to support changes to the union's treaties.
Instead, eurozone members and others will adopt an accord with penalties for breaking deficit rules. It will be backed by a treaty between governments, not an EU treaty.
"In fact, 26 leaders are in favour of joining this effort. They recognise the euro is a common good," said European Council President Herman Van Rompuy.
Mr Cameron said he had done "the right thing" by not signing up to the deal, as it was not in Britain's interests.
"We were offered a treaty that didn't have proper safeguards for Britain, and I decided it was not right to sign that treaty," he told the BBC.
"We're still in the single market. That is the best safeguard of keeping markets open," he said.
German Chancellor Angela Merkel said the UK was the only country to have expressed reservations, but that Mr Cameron had recognised that a stable euro was in Britain's interest.
Of the nine other EU countries outside the euro, Hungary, the Czech Republic and Sweden have said they must consult their parliaments. Six others - including Denmark, Poland and Latvia - have agreed to join the new deal.
However, some countries - such as the Republic of Ireland, which is in the eurozone - have a constitutional requirement to hold a referendum on any major transfer of powers to the EU.
The Irish Minister for European Affairs, Lucinda Creighton, told the Reuters news agency the probability of a referendum was "50-50 and we will be looking at the detail over the next couple of weeks".
EU leaders aim to have the pact - known as a "fiscal compact" - ready to take effect by March.
Its main provisions include:
- a cap of 0.5% of GDP on countries' annual structural deficits
- "automatic consequences" for countries whose public deficit exceeds 3% of GDP
- the tighter rules to be enshrined in countries' constitutions
- the EU's permanent bailout facility, the European Stability Mechanism (ESM), to be accelerated and brought into force in July 2012
- the adequacy of 500bn-euro (£427bn; $666bn) limit for the ESM to be reassessed
- eurozone and other EU countries to provide up to 200bn euros to the International Monetary Fund (IMF) to help debt-stricken eurozone members
The BBC's Europe editor Gavin Hewitt, in Brussels, says the new pact will be quicker to set up than a change to the treaty but it may prove less rigorous.
But, he says, Europe has taken a big step towards closer integration, with binding rules over tax and spending, and sanctions against countries that overspend.
Nearly 10 hours of talks could not produce an agreement involving all member states.
French President Nicolas Sarkozy said the sticking point had been Mr Cameron's insistence on a protocol allowing London to opt-out on proposed change on financial services.
"We could not accept this," he said.
IMF chief Christine Lagarde welcomed the deal as "a really good step in the right direction".
But the announcement from Brussels failed to lift the markets, which are still hoping for more intervention by the European Central Bank (ECB), and European stocks traded slightly down on Friday.