The German company’s camera-based, ball-tracking system GoalControl-4D uses 14 high-speed cameras which are located around the pitch and directed at both goals.
If successful at the 16-match Confederations Cup this summer, it will be installed at the stadia hosting World Cup matches next year.
Football’s rule-making panel approved goal-line technology last July.
Fifa President Sepp Blatter pushed for it to be used in Brazil after England midfielder Frank Lampard’s disallowed against Germany at the 2010 World Cup.
GoalControl was selected ahead of three other companies: GoalRef and Cairos, which both use magnetic fields, and British-based Hawk-Eye, another camera system considered the favourite.
Hawk-Eye is already used in tennis and cricket and its English parent company was bought by World Cup sponsor Sony Corp before it began Fifa-endorsed testing in 2011.
All four systems met Fifa’s demand that a signal is transmitted to the referee’s watch within one second if a goal should be awarded.
Sky Sports Presenter Celina Hinchcliffe said: “It comes somewhat as a surprise because GoalControl was the last of the contenders to join the race for the contract.
“It is interesting to point out that Fifa have awarded the contract to GoalControl rather than systems linked to their sponsors Sony (Hawk-Eye) or Adidas (GoalRef).”
Fifa said: “While all four companies had previously met the stringent technical requirements of the Fifa quality programme, the final decision was based on criteria relating more specifically to the tournaments in Brazil.
“(This included) the company’s ability to adapt to local conditions and the compatibility of each GLT (goal-line technology) system in relation to Fifa match operations.
“The respective bids were also judged on cost and project management factors such as staffing and time schedules for installation.
“The use of GoalControl-4D in Brazil is subject to a final installation test at each stadium where the system will be installed.”