The provisional agreement, announced by diplomats and officials after late-night talks between EU country representatives and the European Parliament, means bankers face an automatic cap on bonus payouts at the level of their salaries.
If a majority of a bank's shareholders vote in favour, that ceiling can be raised to two-times pay.
"For the first time in the history of EU financial market regulation, we will cap bankers' bonuses," said Austrian MEP Othmar Karas (European People's Party), who helped negotiate the deal.
Such limits to bankers' pay, which is set to enter EU law as part of a wider overhaul of capital rules to make banks safer, will be popular on a continent struggling to emerge from the ruins of a 2008 financial crisis.
But it represents a setback for the British government, which had long argued against such absolute limits. The City of London, the region's financial capital with 144,000 banking staff and many more in related jobs, will be hit hardest.
As it stands in draft legislation, the cap would also apply to bankers employed by an EU institution but based elsewhere globally, in a centre such as New York, according to one official.
There are also provisions for adjusting the value of long-term non-cash payments, so that more bonus can be paid in that way without breaking through the new ceiling.
Ireland, which holds the rotating EU presidency and negotiated what it called a "breakthrough," will now present the agreement to EU countries.
The backing of a majority of EU states is needed for the deal to be finalised. One member of the European parliament privately signalled that the deal could yet change, pointing to the "reservations" of some EU countries.
Irish Finance Minister Michael Noonan said he would ask his peers to back it at an EU ministers' meeting on 5 March in Brussels.
The change in the law is set to be introduced as part of a wider body of legislation demanding banks set aside roughly three times more capital and build up cash buffers to cover the risk of unpaid loans, for example.
Some experts have criticised the EU, however, for failing to keep to all of the so-called Basel III code of capital standards drawn up by international regulators to reform banking after the financial crash.
The agreement on Thursday will also require banks to outline profits and other details of operations on a country-by-country basis.
A ceiling on bonuses, the only one of its kind globally, is perhaps the most radical aspect of the new rules.
Many in banking argue, however, that such reform will do little to lower pay in finance, where head-hunters say some annual packages in London approach 5 million pounds (€5.77 million).
"If the cap is implemented, it could result in significantly more complex pay structures within banks as they try to fall outside the restrictions to remain competitive globally," said Alex Beidas, a pay specialist with the law firm Linklaters.
An earlier attempt to limit bankers' pay with an EU law forcing financiers to defer bonus payments over up to five years merely prompted lenders to increase base salaries.
But it would be harder for banks to raise base pay this time around. The bonus rules will come as part of wider legislation setting higher capital standards for banks, increasing their costs and curbing freedom to hike salaries.