Tom Hanks is starring as an American lawyer tasked with rescuing a pilot downed in the Soviet Union, said The Hollywood Reporter.
Stowell, 29, will play the pilot, Francis Gary Powers. In real life, Powers' spy plane was shot down over Soviet airspace in 1960. He was captured and sentenced to 10 years in prison, prompting the US to attempt to get him home.
This marks the second Spielberg project for Stowell.
20th Century Fox and DreamWorks are co-financing the film, with Fox handling international distribution. Disney is handling domestic distribution. The film hits US theatres October 16, 2015.