The move came ahead of a 17:00 BST regulatory deadline to close the deal.
It followed days of talks between the UK, French and German governments to overcome political objections.
The UK wanted its counterparts to agree to limit their influence in the merged firm in order to maintain BAE’s strong working relations with the US Pentagon.
“We are obviously disappointed that we were unable to reach an acceptable agreement with our various government stakeholders,” said BAE chief executive Ian King.
EADS head Tom Enders said: “A special thank-you goes to Ian King for his trust and partnership. It is, of course, a pity we didn’t succeed but I’m glad we tried.”
BAE shares fell 2% in London trading as the news broke, while EADS shares jumped 3%.
UK firm BAE and Franco-German Airbus-owner EADS had to decide by shortly after the end of the London trading day on Wednesday whether to ask the Takeover Panel for an extension to their $45bn (£28bn) merger talks.
However, our business editor said that the decision did not rule out the possibility that talks between the two companies’ management might reopen in a few months’ time.
UK Defence Secretary Philip Hammond had been meeting his French and German counterparts in Brussels. The merger needed the approval of the UK, French and German governments.
Only the French government has a direct stake in EADS, but Germany also exerts a high degree of control through the shareholding of German industrial group Daimler. The British government is able to veto any deal through its ownership of a “golden share” in BAE.The BBC business editor said that the outlook for the deal was already looking fairly bleak on Tuesday night, in large part because Germany had dug its heels in.
He noted that BAE’s board had made it “an absolute condition for the transaction that the French and German governments should never own more than 9% each of the merged outfits, that they should not vote as a bloc and that they should not have representatives on the holding company board”.
However, the key sticking point appears to have been the insistence by the UK government and the two company heads that directors appointed by the French, German and UK governments should not sit on the top board of the merged group.
The deal would have created a European aerospace and defence giant comparable in size to Boeing of the US.
The two company bosses said in their joint statement announcing the cessation of merger talks that: “The merger would have produced a combined business that would have been a technology leader and a greater force for competition and growth across both the commercial aerospace and defence sectors.”
They said that full commercial details of the merger – including the legal structure, management, and the logistics of combining the businesses – had already been fully worked out between the two of them before the politicians weighed in.
But the merger talks then became bogged down by wranglings between their respective governments after the deal became public on 12 September.
The UK government was thought to broadly back the deal, particularly as it would help to protect jobs at two factories in the UK that are owned by EADS, that manufacture wings and other parts for Airbus planes.
It would also have helped BAE, which was suffering from defence spending cuts by the US and UK, its two main customers.
The US government was reportedly concerned about French and German influence over the merged firm. BAE is already active on classified research and development projects for the US military.
However, even if a political agreement had been reached, the deal still faced opposition from BAE’s largest shareholder, fund manager Invesco Perpetual, which said on Monday that it had “significant reservations” about the proposed merger and “does not understand the strategic logic” of the deal.
Invesco, which owns 13.3% of BAE, did not appear to be alone. The Financial Times reported on Tuesday that more than 30% of the UK firm’s shareholders had expressed qualms.
French media group Lagardere, which manages the French government’s stake in EADS, had also claimed that the financial terms of the merger are unfavourable.