Annan was raised in the North End area of Detroit, Michigan. His mother is African American and was raised in the south, and his father is Ghanaian. He wanted to pursue acting from a young age and studied improv and theater from youth. When he was 17 he joined a dance troupe. Annan received his diploma from Cass Technical High School and studied theater at State University of New York-Purchase, where he received his Bachelor of Fine Arts degree.
After college, Annan was hired as the choreographer in residence at the Yale School of Drama. He also performed in theater productions on and off-Broadway. He moved to Los Angeles in 2014 to pursue television acting. Annan has appeared in Claws, Shameless, This is Us, and Snowfall. He is also the choreographer for the series All American.
In 2009, Annan's friend recommended him for a role in Pussy Valley, a play by Katori Hall centered on a strip club in the Mississippi Delta. Annan auditioned for and was cast as Uncle Clifford, the club's non-binary owner. He developed a detailed backstory for the character and portrayed the role in several smaller runs as well as the full production at Mixed Blood Theatre in 2015.

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