The Commission said a technical agreement had been reached with Greece, which now requires political approval.
Earlier, Greece’s Finance Minister Euclid Tsakalotos had said “two or three small issues,” were yet to be resolved with lenders, following overnight talks in Athens.
A deal is needed to keep the country in the eurozone and avert bankruptcy.
The Greek government is hoping to push a new €86bn (£60bn) three-year agreement through parliament later this week.
The country needs a deal by 20 August, when it has a debt repayment of about €3bn to make to the European Central Bank.
A European Commission spokeswoman said a technical deal had been reached last night between parties including Greece, the International Monetary Fund and the European Central Bank.
She said a series of phone calls between political leaders would now take place.
Both issues had been key sticking points in negotiations.
“Finally, we have white smoke,” the official said.
Deregulation of the natural gas market, another sticking point, was also agreed.
But Finnish Finance Minister Alexander Stubb sounded a cautious note, saying more work needed to be done with the details to finalise the agreement.
The Eurogroup of eurozone finance ministers is to meet on Friday to discuss approval of the deal, Spanish Prime Minister Mariano Rajoy said.
His centre-right People’s Party, which has a majority in the Spanish parliament, will be asking other parties to vote in favour of the agreement, he added.
Greek bailout deal – some key points*
Phasing out early retirement and gradual increase of pension age to 67 by 2022
Agreement to recapitalise banks and manage non-performing loans
Deal on primary surplus targets: 0.25% deficit for 2015, 0.5% surplus in 2016, 1.75% in 2017 and 3.5% in 2018
Review of Greek social welfare system with aim of cutting expenditure
Deregulation of gas market by 2018; privatisation plans for ports at Piraeus and Thessaloniki
Opening up of professions and tightening definition of who is a farmer
Increase in tax on shipping
The really hard negotiations start soon – on how to reduce Greece’s massive debts, set to peak at close to 200% of GDP or national income in the next two years (according to the IMF) to an affordable level.
Without debt write-offs, prosperity will never return to Greece, and its future in the euro will never be assured.
With debt write-offs, populist parties throughout the eurozone will be able to claim to voters that they have nothing to fear and everything to gain from throwing out the mainstream establishment parties and re-asserting national sovereign rights to economic self-determination.
Or to put it another way, euro politics and euro economics of Greek debt forgiveness point in diametrically opposed directions.
Which is why no-one should see today’s important bailout agreement for Greece as a permanent happy ending.
Vicky Pryce, chief economic adviser at the Centre for Economics and Business Research in London, told the BBC that so far the Syriza prime minister Alexis Tsipras had managed to get support for the third bailout by relying on his opposition parties, which are “determined to see that the whole thing is actually sorted out, so that’s not a very sustainable situation for the future”.
Though the radical left-led government was elected on a staunchly anti-austerity platform in January, it was forced into a policy U-turn after bailout talks came close to collapse last month.
25 January: Syriza wins the general election on an anti-austerity platform
21 February: Eurozone finance ministers extend Greece’s financial rescue programme by four months, just days before the previous programme ends
27 July: PM Alexis Tsipras calls a referendum for voters to decide whether to accept a new bailout deal offered by international creditors
28 July: ECB freezes liquidity lifeline
29 June: Greek banks close after government introduces capital controls, with individuals only allowed to withdraw €60 a day
30 June: Eurozone bailout expires, Greece misses €1.6bn payment to IMF
5 July: Greeks vote against a new bailout offer in referendum
13 July: Eurozone leaders agree to offer Greece a third bailout conditional on Greece’s parliament passing tough reforms
16 July: Eurozone ministers agree a €7bn (£5bn) bridging loan for Greece
20 July: Banks reopen after three weeks but restrictions on transfers and withdrawals remain
11 August: Greece says third bailout deal broadly secured