Wright was born in Washington, D.C., to a mother who worked as a customs lawyer and a father who died when Wright was a child. He graduated from St Albans School and attended Amherst College, receiving a bachelor's degree in political science and planning to attend law school; however, he decided to study acting instead. After attending New York University for two months, he left to became a full-time actor.
Wright began appearing off-Broadway in New York City and Washington DC, and in 1990, he appeared in his first major film as an attorney in Presumed Innocent, which starred Harrison Ford. In 1991, Wright joined John Houseman's national touring repertory company The Acting Company with productions of A Midsummer Night's Dream and Athol Fugard's Blood Knot. Wright continued with his stage performances and in 1994 was cast as Norman "Belize" Arriaga in Tony Kushner's award-winning play Angels in America. His portrayal of a gay nurse forced to take care of the homophobic Roy Cohn as he lay dying from AIDS won him the Tony Award for Best Featured Actor in a Play.
In 1996, Wright portrayed painter Jean-Michel Basquiat in the film Basquiat.
Wright's performance was again critically acclaimed. Throughout the
1990s and early 2000s, Wright appeared in both leading and supporting
roles in such films as Celebrity (1998), Ride with the Devil (1999), Shaft (2000), and Boycott (2001), where he gave an AFI Award-winning performance as Martin Luther King, Jr.. In 2003, Wright reprised his role as Norman "Belize" Arriaga in HBO's award-winning adaptation of Angels in America. His performance garnered him an Emmy award as well as a Golden Globe award for Best Supporting Actor in a miniseries. In 2004, he appeared in Jonathan Demme's remake of The Manchurian Candidate. In February 2005, Wright returned to HBO Films in Lackawanna Blues. He also guest starred on The Young Indiana Jones Chronicles and Homicide: Life on the Street.
Among his other film roles was Washington attorney Bennett Holiday in Syriana (2005). The same year, he played Bill Murray's eccentric Ethiopian neighbor Winston in Broken Flowers. In 2005, he starred in the play This Is How It Goes. He also appeared as one of the tenants in Lady in the Water. In 2006, Wright featured as Felix Leiter in the James Bond movie Casino Royale. He reprised the role in Quantum of Solace.
In 2007, Wright starred in the alien invasion suspense thriller The Invasion. In 2008, he portrayed Colin Powell in W. He portrayed Muddy Waters in Cadillac Records, a biopic, loosely about the rise and fall of Chess Records. In 2010, Wright played Jacques Cornet in the world premiere run of A Free Man of Color at the Vivian Beaumont Theater of the Lincoln Center for Performing Arts in New York City.
Wright has also been announced as playing Beetee in The Hunger Games films, starting with The Hunger Games: Catching Fire, which is due to start filming in September 2012.
Wright married actress Carmen Ejogo in August 2000. They have a son named Elijah and live in Brooklyn, New York. In 2004, Wright received an honorary degree from his alma mater, Amherst College.
Wright has been a longtime activist working to end resource-related
conflicts. In 2011, Wright established Taia Lion Resources, a mineral
exploration company focused on ethical and sustainable mining in Sierra
Leone. In August 2012, Wright's conflict-free mining philosophy was highlighted in a video by the Enough Project.