EADS and ThyssenKrupp will pay around 145 million euros ($172 million) in cash and assume Atlas Elektronik's pension liabilities of 72.4 million euros.
ThyssenKrupp Technologies will own 60 percent of Atlas Elektronik, which makes sonar equipment for submarines and ships, while EADS will hold the remaining 40 percent.
ThyssenKrupp and EADS had been widely expected to win the bidding race for the company, with sources close to the matter telling Reuters earlier this month that a deal was due soon.
The result was nevertheless a setback for France's Thales, which had also been bidding but ran into political objections to a foreign firm obtaining majority control.
Germany's DaimlerChrysler has a 30 percent stake in EADS, the parent firm of the Airbus plane consortium. BAE shares closed down 1.6 percent at 381-3/4 pence. ThyssenKrupp fell 0.1 percent to 17.62 euros by 1537 GMT while EADS shed 1.9 percent to 31.94 euros. Thales dropped 1.3 percent to 38.19 euros.
BAE, Europe's largest defence equipment company, put Atlas up for sale earlier this year, which some analysts said indicated a shift in focus to the larger US defence market.
The take-over of the Bremen-based company comes as Europe's naval shipbuilding industry starts to consolidate in the face of stiff global competition.