The deal will create Europe's largest guided weapons business, Matra BAe Dynamics, with annual turnover of around pounds 1bn and a pounds 2.6bn order book. It will employ about 6,000 people.
BAe and Lagardere said the signing marked a big step forward in the consolidation of the European defence industry.
It will enable the industry to compete against US giants such as Lockheed Martin, which have emerged from a series of multi-billion dollar mergers in recent years.
Analysts gave the joint venture the thumbs-up: "Putting these two businesses together makes a lot of sense," said Guy Kekwick, aerospace analyst at Lehman Brothers. "The deal gives critical mass to British Aerospace's Dynamics (missiles) business which has been missing for some time."
The companies said they hoped Matra BAe Dynamics would draw in Thomson SA's guided weapons business if Lagardere succeeded with a proposed bid to buy the French state-owned defence and consumer electronics firm as part of a privatisation programme.
Under the final details of the deal, BAe will make an initial cash payment to Lagardere of pounds 80m to reflect the current difference in value between Lagardere's Matra Defence and BAe Dynamics.
But the final amount to be paid will be adjusted to no less than pounds 50m and no more than pounds 110m, depending on who wins which orders over the next four years.
The announcement is the culmination of more than three years of negotiations between the two companies, which first announced that they were in talks in early 1993.
Industry sources said it was widely believed that political factors delayed the deal. The breakthrough came when Britain announced last month that it would buy Matra's Apache air-launched cruise missile in an order worth pounds 800m, to be awarded to the BAe/Matra joint venture.
The joint venture is still subject to governmental and regulatory approval and both companies said it might be some months before it went ahead, Both are, however, confident of securing approval.
The head of BAe Defence, John Weston, will be chairman at Matra BAe, with Noel Forgeard, chief executive at Matra Defense Espace, as chief executive. BAe's finance director, Richard Lapthorne, and Phillipe Camus, the Lagardere director, will complete the four-man board.
British Aerospace shares closed up 11p at 964p.