Smith is a native of Allen, Texas. He studied at the Quad C Theatre program at Collin County Community College in Plano, Texas. After he was an apprentice for one year at Stephens College in Columbia, Mo. Smith then moved to New York City to attend the Juilliard School Drama Division's four-year acting program (Group 36: 2003–2007), where one of his classmates was Nicole Beharie. Smith graduated from Juilliard with a Bachelor of Fine Arts degree.

While enrolled at Collin College, Smith worked as theatre technician. He was later cast as Alex in A Clockwork Orange in a Quad C Theatre production to great reviews. In 2005, he portrayed Trey, a gay man facing intolerance from the son of a fundamentalist preacher, in Hate Crime, an independent film that featured at multiple gay and lesbian film festivals around the United States.

Smith eventually received acting roles in two more independent films, Red Hook and The War Boys. In 2008, he appeared on Broadway in the play Come Back, Little Sheba as the character Turk. Smith was cast as Lieutenant Matthew Scott, a lead role in the 2009 Stargate television series, Stargate Universe, until its cancellation in 2010.

In 2011, Smith recurred on The CW's Gossip Girl and starred in the SyFy original film Red Faction: Origins. In April 2012, he began his run as Andrei in the hit Broadway show, The Columnist, which ended in July 2012. His next projects include the mini-series Coma from Producer Tony Scott and Warehouse 13 for SyFy. He also guest-starred on Law & Order.

In September 2013, he starred in a much-praised production on Broadway of Tennessee Williams's The Glass Menagerie. This role earned him 2014 Drama Desk and Tony Award nominations as Outstanding Featured Actor in a Play.

Smith is a lead cast member on the Netflix original series Sense8 (2015-present). He also appeared in the pilot episode of Quantico as one of the new FBI recruits.