Noel Forgeard will be replaced by Louis Gallois, the president of French railway company SNCF. Gallois will work with the other current co-chief executive of EADS, Tom Enders.
Gustav Humbert, the chief executive of Airbus, also resigned and will be replaced by Christian Streiff, former deputy CEO of French building materials group Saint-Gobain, the company said.
EADS said Airbus would be integrated more closely into the parent company.
Shares in the European aerospace giant fell 26% on June 14, after the company announced the A380 delays and said the production problems would cut 2 billion euros ($2.5 billion) off profits over four years. EADS controls Airbus through an 80% stake
The resigning Humbert said the delays to the A380 had been a "major disappointment for our customers, our shareholders and our employees", adding that he felt offering his resignation was the right course of action.
Forgeard was also under pressure over the controversial sale of EADS stock weeks before the company launched an internal assessment of the superjumbo delays. He made 2.5 million euros ($3.1 million) from the sale.
French stock market regulator AMF is investigating the sale, but Forgeard denies insider dealing.
Forgeard is being investigated
over the sale of EADS stock
EADS has two chairmen and two chief executives - a Frenchman and a German in each post - to preserve a balance of power in the aerospace company.
Thierry Breton, the French finance minister, pushed Gallois, a former head of Aerospatiale, the former state-owned designer of Concorde which now makes up part of Airbus, as sole chairman, but was opposed by French shareholder Lagardere.
Due to an agreement made in 2000, only Lagardere and German shareholder DaimlerChrysler can propose key nominations which the French government can accept or reject. This is designed to limit the influence of the government on the company, in which it has a 15% stake.