The British actor, whose credits include "Pitch Perfect" and "Harry Potter", joins John Krasinski and the recently cast Dominic Fumusa, reported Deadline.
Stroma will star as an undercover CIA agent in Libya in the film, which centers on the attack of a US State Department Special Mission Compound in Benghazi on the anniversary of 9/11.
"The Inbetweeners 2" star Stroma will next be seen in Lifetime's original comedy-drama series UnReal, which is set to premiere on June 1.
James Badge Dale, Max Martini and Pablo Schreiber have also signed on to the project, which is to begin production in Malta and Morocco next month.
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