French President Francois Hollande has said "Europe has won" as a debt deal was struck with Greece.
He said that to have lost Greece as a member would have been to lose "the heart of our civilisation" and called on the Greek parliament to convene within hours to adopt the new package of austerity measures.
Greek banks are expected to remain closed for a few more days while details of the package are finalised.
German Chancellor Angela Merkel said that a deal was struck over the Greek crisis despite the recent loss of trust, which she called, "the most important currency."
This success has come in spite of the fact that in the past few weeks and months, the most important currency, namely trust, was indeed lost between us, but as we all know, paper is patient.
In other words, (going forward) step by step, what will be important will be to implement what we have agreed on during the night. In the opening paragraphs of this document, we point to the fact that trust needs to be rebuilt, that those in charge in Greece have to to take responsibility for what we have decided here politically in order to be able to implement all of it.
The Greek Prime Minister has said his country "will continue to fight to return to growth" after accepting a bailout deal.
Alexis Tsipras told a news conference it had been a "tough battle" with "difficult decisions" but he had managed to "avert a banking system collapse" and stay in the Euro.
The terms of the deal will include debt restructuring and a debt package of €35bn.
Greece will see a 'key loss of sovereignty' with the €50bn fund, as part of the eurozone deal, ITV News Economics Editor Richard Edgar reports:
Key concession seems to be the 50bn fund set up with privatisation of Greek assets. Key loss of sovereignty
"Trust can be regained" says Merkel - but it's not yet, note.
Austrian PM says Tsipras relented and has allowed IMF involvement in the bailout of - another v symbolic concession.
Jean-Claude Juncker, the president of the European Commission, has said there will not be a "Grexit" after agreement was reached on a new Greece debt deal following "laborious" talks in Brussels.
ITV News' Richard Edgar reports:
Juncker "there is no Grexit"
Juncker - the agreement was laborious"!
Today, we had only one objective: to reach an agreement. After 17 hours of negotiations, we have finally reached it. One can say that we have 'agreekment'. Leaders have agreed in principle that they are ready to start negotiations on an ESM programme, which in other words means continued support for Greece.
There are strict conditions to be met. The approval of several national parliaments, including the Greek parliament, is now needed for negotiations on an ESM programme to formally begin.
Nevertheless, the decision gives Greece a chance to get back on track with the support of European partners.
Questions remain over the Greek deal as it must still be approved by the Greek parliament.
ITV News Economic Editor Richard Edgar reports:
Dijsselbloem is setting out plans for next few days: Greek parliament has to approve package 1st. Big question hangs over this
Dijsselbloem - Greek product and labour market reforms still need work.
Dijsselbloem - "trust was a very key issue"
The deal reached over the Greek deal was a 'unanimous' agreement, EU President Donald Tusk has said.
Eurozone leaders have reached agreement, after a marathon emergency summit on Greece.
"Agreement," Belgian Prime Minister Charles Michel said in a one-word tweet.
The Cyprus government spokesman also tweeted: "Seems we have a deal."
The future of Europe is balanced on a knife-edge, the head of the European Parliament Martin Schulz said after eurozone leaders failed to reach a deal on Greece at an emergency summit.
"Today the European project is on a knife edge," Schulz, a member of Germany's Social Democrats (SPD), told Deutschlandfunk radio.
"In Brussels, things are on a knife edge and the eurozone could fly apart," added Schulz, who said the SPD wanted Greece to stay in the euro.
Turning to an idea floated by the German Finance Ministry for Greece to temporarily exit the euro, Schulz said: "This five-year exit idea is off the table. We don't need to talk about that anymore."
Despite emergency talks through the night no deal has been reached between eurozone leaders to resolve the Greek crisis.
The Athens government is desperate for a resolution to avoid a meltdown of its banking system.
Several officials have reportedly said there are still wide differences among the 19 leaders of the eurozone countries on the terms of a third bailout.
A draft proposal put to the eurozone leaders even raises the prospect of a temporary Grexit, referring to a "time-out from the euro area" if no deal can be reached.
Greece has asked Europe's bailout fund for a three-year 53.5 billion euro (£38.4 billion) financial package but many officials in Brussels say the figure will have to be much higher and insist on tough austerity measures.