Wright was born in Washington, D.C., the son of Barbara Evon, a customs lawyer, and James Charles Wright, Jr., who died when he was a child. He graduated from St. Albans School and attended Amherst College, receiving a bachelor's degree in political science and planned to attend law school; however, he chose to study acting instead. After attending New York University for two months, he left to become 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. In 1993 and 1994, he appeared 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 Roy Cohn as he dies of 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, to critical acclaim. Throughout the 1990s and early 2000s, Wright appeared in both leading and supporting roles in such films as Celebrity, Ride with the Devil, Shaft, and Boycott, 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 '. Among his other film roles was Washington attorney Bennett Holiday in Syriana. 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 was featured as Felix Leiter in the James Bond movieCasino Royale. He reprised the role in Quantum of Solace and will so again in the upcoming Bond movie No Time to Die due out in November of 2020. In 2007, Wright starred in the alien invasion suspense thrillerThe Invasion. In 2008, he portrayed Colin Powell in W. He portrayed Muddy Waters in Cadillac Records, a biopic, loosely based on 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 plays Beetee in The Hunger Games film series, starting with ', released in November 2013. He also landed the role of Dr. Valentin Narcisse in season 4 of Boardwalk Empire, starting in the fall of 2013. Wright was twice nominated for the Emmy for his performance as Bernard Lowe in HBO's Westworld. In March 2017, Wright appeared in a commercial for Dell Technologies. In 2018, Wright produced the HBO documentary We Are Not Done Yet, which gives voice to war veterans who, through a USO-sponsored arts workshop at Walter Reed National Military Hospital, discover the power and healing of shared experience to unite and find resilience in the face of post-traumatic stress. Wright starred in as the leader of the Washington Liberation Front, a militant group. The game was released on June 23rd 2020.
Wright married actress Carmen Ejogo in August 2000. They had a son named Elijah and a daughter named Juno and lived in Brooklyn, New York. They have since divorced. In 2004, Wright received an honorary degree from his alma mater, Amherst College. In 2011, Wright established Taia Lion Resources, a gold exploration company which labels itself as being involved in ethical and sustainable mining in Sierra Leone. However, it has been reported that the organization has experienced significant financial problems, that those who worked for Wright's organization have gone without pay for months and were not provided adequate supplies for their jobs, and that only 2-3 percent of any profits from the endeavor would be reinvested in the local community.