The job cuts, part of a major restructuring in the face of falling orders, will affect the group's workforce in Germany, France, Spain and Britain over the next three years, the company said in a statement.
An industry source said about 2,600 of the job cuts would be in Germany, around 1,700 in France, 700 in Britain and another 600 in Spain.
The news came after a meeting of its European works council with chief executive Tom Enders, whose bold plan to merge the conglomerate with Britain's defence group BAE Systems was torpedoed last year with a surprise veto by Germany.
"We need to improve our competitiveness in defence and space – and we need to do it now," Enders said in a statement.
"With our traditional markets down, we urgently need to improve access to international customers, to growth markets. For that to work, we need to cut costs, eliminate product and resource overlaps, create synergies in our operations and product portfolio and better focus our Research and Development efforts."
He added: "That's what the restructuring and integration plan for our defence and space business is all about."
However, France's Labour Minister Michel Sapin insisted later that despite the thousands of defence job losses at EADS there would be no forced layoffs.
Speaking on French television he said that efforts would be made "to slide personnel who currently work in armaments towards the civil sector."
He said: "Not one single person is going to the unemployment centre as within the group itself there are jobs being created."
Anticipating fierce resistance from labour representatives, the company said it would do what it could to cushion the impact of the cuts, due to be completed by the end of 2016.
Furloughed employees will be offered redeployment in 1,500 jobs at the company's Airbus and Eurocopter divisions.
About 1,300 short-term contracts will not be renewed, and with voluntary measures, the company estimated final redundancies to come in at between 1,000 and 1,450 employees.
"The group also intends to enter into negotiations with its works councils to seek agreements on labour cost reductions which could help mitigate the social impact of the restructuring plan," it added.
EADS has previously announced that it is changing its name to Airbus to raise its public profile.
The overhauled defence and space division, to be called Airbus DS, will have a streamlined legal structure to cut costs and be up and running by January 1st, the company said.
Shares in EADS rose 0.82 percent to €50.49 in Paris on the news. But a French union, the FO Metalworkers' Federation, reacted angrily to the announcement, protesting that EADS on the whole "is doing well financially and its order books are in good shape".
It said the group's focus on improving its profit margin should not come at the expense of its staff and urged the French state as a major shareholder to fight to protect jobs.
"FO calls on EADS to avoid layoffs and appeals to its sense of responsibility and solidarity so that no employee will be left behind," it said.
Enders has stressed that the company cannot continue with business as usual while government clients are increasingly resorting to cuts to the military to shore up strained public finances.
In November, Germany's biggest union IG Metall held industrial action as a warning against the company's expected restructuring plans.
IG Metall's Rüdiger Lütjen, who is head of EADS' European works council, said in a statement the union was unhappy that forced redundancies had not been excluded from the restructuring plan.
These "aren't an option" when EADS is highly profitable, said Lütjen, adding, "competitiveness isn't increased when one loses highly qualified and motivated people".
But the overhaul is seen by management as unavoidable after the failed plan to merge with BAE.
That was shelved after objections from Germany, which had worried it would trigger major job losses.
The success of the Airbus division came after a radical restructuring in 2007 in a plan that originally called for 10,000 job cuts, but in the end cost 7,900 jobs.