The deal would create a global aerospace and defence giant in a sector facing challenges and uncertainties amid cuts to government defence budgets in Europe and the United States.
The merged companies would have combined sales of more than €70 billion ($90.3 billion) and more than 220,000 employees.
EADS is already one of Europe's biggest companies, parent to planemaker Airbus, helicopter maker Eurocopter, satellite builder Astrium and defence electronics contractor Cassidian.
Airbus and EADS have long been rivals to U.S.-based Boeing Co. in civil and defence aviation. The proposed deal is a clear shot at catching up to Boeing's defence business — and passing it.
The U.S. and European firms have fought ruthlessly in the courts over government subsidies, and competed for years for a huge contract to build new aerial refuelling tankers for the U.S. Air Force, a contract Boeing finally won.
Boeing's defence and space business had revenue last year of almost $32 billion, from selling Chinook helicopters and F-18 fighter jets to the U.S. and, increasingly, other countries.
Defence revenue at EADS was a little more than half as much — but by adding BAE, the combined company would have a defence business significantly bigger than Boeing's.
EADS gets only about one-third of its revenue from defence — something that CEO Louis Gallois has said he wants to change.
BAE and EADS confirmed discussions in a statement to the London Stock Exchange, saying that under the proposed merger, BAE Systems shareholders would own 40 per cent and EADS shareholders 60 per cent of the enlarged group.
The deal would unite the companies' boards and management but they would continue to be listed separately on stock exchanges, the statement said.
BAE and EADS pointed to a "long history of collaboration" on projects such as the Eurofighter Typhoon jet, which is partly assembled in Britain and then built by EADS elsewhere in Europe.
EADS would have to pay 200 million pounds ($322.1 million) to its shareholders prior to the completion of any deal in order to align the companies' different dividend payout policies.
U.K.-based BAE and Netherlands-based European Aeronautic Defence & Space Company acknowledged the sensitive nature of their global businesses and said they had initiated discussions with "a range of governments" about the implications of a merger.
IHS Jane's analyst Guy Anderson said the proposed deal would change the European defence market beyond recognition, which could pose a tough sell for regulators.
"This is potentially bigger than the Euro merger of '99 which created EADS," Anderson said. "The call for consolidation to save the European defence industries has been ringing out for years now, and with this it appears to be happening in a bigger way than ever hoped."
With BAE and EADs already co-operating on Eurofighter and owning two of the three parts of the MBDA missile making group, a merger would change ownership structures across Europe, and Anderson said regulators would need convincing that it won't crush competition.
"It will probably take a while to unravel all the details and find the actual degree of overlap," Anderson added.
EADS is jointly French and German-owned — though incorporated in the Netherlands — with dual headquarters in Munich and Paris as well as the Airbus headquarters in Toulouse, France. It already has to manage political considerations when it makes decisions such as where to build a factory, said Cai von Rumohr, an aerospace analyst at Cowen & Co.
"There's always political machinations between the French and the Germans," he said. "Now if you put the British in the mix, I think that's going to get further complicated."
The British government said it was aware of the proposed deal and was working with both companies "to ensure that the U.K.'s public interest was properly protected."
The companies said they envisioned that certain defence projects of each company "would be ring-fenced with governance arrangements appropriate to their strategic and national security importance."
They also envisioned issuing special shares in BAE and EADS to each of the French, German and U.K. governments to replace existing government stakes in the two companies.
Any agreement on the terms of merger would require approval by the boards of both companies, according to the stock exchange statement.
The companies have until Oct. 10 to announce a deal or walk away from a merger.
BAE, which produces Astute nuclear-powered submarines and is the largest supplier of land vehicles to the U.S. army, last month reported a slight dip in first-half profits and cautioned about its U.S. outlook amid uncertainty over defence spending ahead of November's presidential election.
BAE shares closed up 10.6 per cent at 3.63 pounds ($5.84) on the London Stock Exchange. In Paris, shares of EADS dropped 5.6 per cent to 28 euros ($36.11).
Associated Press writers Angela Charlton in Paris and Jill Lawless in London, and AP Business Writer Joshua Freed in Minneapolis contributed to this report.