Streiff's resignation comes after just 100 days in the post as Airbus chief, parent company, EADS said on Monday.
EADS said: "The board of directors at EADS has named Louis Gallois as Airbus chief executive, with immediate effect."
It said that Gallois would "keep his functions as EADS chief executive" alongside German counterpart, Thomas Enders.
"The new structure will allow for simpler and more effective management."
Christian Streiff said he quit as Airbus chief executive because of the way the company was run, saying rumours about him wanting to take the top job at car maker PSA Peugeot Citroen had nothing to do with his decision.
"I progressively came to the conviction that the governance of Airbus did not allow my plan to succeed," Streiff said in an interview to appear in French daily Le Figaro on Tuesday.
The shake-up has occurred after further delays to the A380 superjumbo programme were revealed.
The A380 programme is almost two years behind schedule, saddling EADS with a future cash shortfall of $8 billion.
Streiff's plan to revitalise the manufacturer called for job cuts and a sweeping reorganisation that would have cut productions costs by $2.6 billion.
He also promised to redistribute operations among European production sites.
In addition to delays with the A380 and possible problems with the A350, Airbus is also facing potential snags with its planned A400M military transport plane.
A German based analyst believes the news will harm the price of EADS's shares. Speaking from Frankfurt, Germany, he said: "EADS is tumbling from one catastrophe to the next."
The French state has a 15 per cent stake and the French media and defence group Lagardere, hold 7.5 per cent.
Germany is represented by automaker DaimlerChrysler, with a 22.5 per cent interest.