Work under the initial $8.5 million award is already underway, BAE said in its announcement.
BAE Systems said the study focuses on the aerodynamic properties of carrying the missile through a series of wind tunnel tests and developing the pathway for integration of the MBDA weapon.
As an added benefit, the study will explore a common launcher approach for the missile, which could also be used for other multiple weapons.
"With a proven track record on RAF Tornados, the Brimstone 2 weapon offers uncompromising precision and a flexible capability that meets the emerging threats of modern warfare," said Mark Bowman, chief test pilot for BAE Systems. "The Typhoon pilot will be able to confidently engage a wide range of target types including fast moving vehicles.
"When integrated, Brimstone 2 will be another significant development step for Typhoon, enhancing the aircraft's credentials and relevancy going forward."
Brimstone 2 is a low-collateral damage, close air support weapon and has been used by Britain's Tornado aircraft in Afghanistan and Libya.
Britain plans to integrate the missile on Typhoons by 2018.