Boseman, 39, is known for his work in the films 42 and Get On Up. He will soon be seen in Captain America: Civil War.
Marshall served as an Associate Justice of the U.S. Supreme Court 1967-91. He was the first African-American member of the panel and died in 1993 at the age of 84.
"Thurgood Marshall was a man who took his life in his hands every time he came to a town to bring justice," Hudlin said in statement Wednesday.
"Marshall was a cowboy who used his law books as guns. He was the smartest guy in the room of any room he was in. But he wasn't a punk and didn't hesitate to throw a punch if the occasion called for it. It's exciting to have Chadwick bring his extraordinary gifts to this remarkably relevant story."
Marshall began production in Los Angeles this week. It will break for the holidays, then resume principal photography in the spring after Hudlin completes his producing duties for the 88th Annual Academy Awards.