Banks will need to have a core Tier 1 capital ratio of at least 6% under the health check, one of the sources said.
The test will assess if 91 European banks are strong enough to withstand a second economic downturn.
Under the agreement, each bank will publish its result at 1600 GMT on 23 July, and the London-based Committee of European Banking Supervisors (CEBS) will issue a statement summing up the outcome a minute later, several sources said, asking not to be named.
That should provide time over the weekend to digest the results and also time to deal with any trouble spots, industry sources said.
Banks have rebuilt capital in the last 18 months and major banks have lifted their core Tier 1 ratio - a measure of banks' financial strength - above 6%, which many see as the minimum accepted by market investors.
The main criterion of the test will be to have a certain minimum capital level even in adverse economic conditions, sources said.
Exposure to sovereign debt risk will be the second indicator in order of importance.
The final details of the tests will be discussed on 22 July at a teleconference of senior finance ministry officials from EU countries and representatives of the European Commission and the European Central Bank.
Reassuring noises
International Monetary Fund chief Dominique Strauss-Kahn said the tests should not reveal any major problems among the big names, although it was possible that some smaller banks would have to be recapitalised.
"I get the feeling that what will come out will be rather reassuring, and that we'll see that all the big European banks are sufficiently solid to resist any earthquake," he told a French television station.
Jean-Claude Juncker, chairman of eurozone finance ministers group, offered similar reassurance, telling Austrian newspaper Kurier in an interview: "I am not expecting any big catastrophes."
However, if all major banks pass then it could raise questions on whether the tests are severe enough.
"The problem is it seems all the banks are going to pass and I don't think that's credible," said Arturo de Frias, analyst at Evolution Securities in London.
"If Europe goes for the easy solution and says only a couple of cajas in Spain or landesbanks in Germany fail and everybody else is fine [...] then that's not really a stress test."
"I think it's important for Europe to get some confidence in the European banks," Citigroup Chief Financial Officer John Gerspach said on Friday after the US bank's results.
"It's of somewhat importance to us, obviously for stability in the system. It would be nice to see the markets calm down. So hopefully the results will be something that everybody can put a good deal of faith in."
Spain's cajas and Germany's landesbanks in the spotlight
The tests are expected to show that Spain's cajas and German landesbanks, the regional lenders, need capital. Analysts have said each of those sectors could be shown to be at least $30 billion short of capital. Lenders in Greece and elsewhere may need to raise modest amounts, analysts estimate.
Greece's central bank chief said on Saturday he expected the country's debt-laden banks to smoothly pass the EU stress tests. "My feeling is that things will go smoothly for the six Greek banks included in the sample," George Provopoulos, governor of the Bank of Greece, said in an interview published in newspaper Imerisia.
Irish Central Bank Governor Patrick Honohan said his country's two biggest banks had already passed domestic stress tests more severe than tests being organised by CEBS, but the process was good to remove "exaggerated concerns about some particular risks".
EU sources would not discuss whether there was agreement on the size of the "haircut" for government bond holdings and how long any failing bank will have to raise funds.
(EurActiv with Reuters.)
