Yune was born in Washington D.C., the son of Wonhui Park and Tom Taeho Yune. He is of Chinese Mongolian Korean descent. His younger brother is actor Karl Yune. Yune was educated at Our Lady of Good Counsel High School, Silver Spring, Maryland, and St. John's Military School. In 1994, he received his degree in finance from the Wharton School of Business. Yune was one of the original hedge fund traders for SAC Capital but left to pursue entrepreneurial ventures.
Yune changed the spelling of his last name from "Yun" to "Yune" for Screen Actors Guild purposes. He made his film debut in 1999, playing Kazuo Miyamoto in director Scott Hicks' film adaptation of David Guterson's post-WWII novel, Snow Falling on Cedars.
Yune co-starred as Johnny Tran, the ruthless leader of a Vietnamese gang in the 2001 Rob Cohen-directed car-racing film The Fast and the Furious. Although met with mixed reviews, the film was an unexpected summer hit and became one of the most well-known movies around the turn of the millennium, and introduced modified Japanese compacts into American popular culture.
In the next year, Yune was launched to the spotlight after portraying James Bond villain Zao, opposite Pierce Brosnan and Halle Berry, in the 20th 007 feature Die Another Day, directed by Lee Tamahori. Yune was Chosen for the part at age 31.
In 2008, Yune wrote, produced, and starred (as a Bangkok assassin) in the action/adventure movie The Fifth Commandment, directed by Jesse V. Johnson and also stars Keith David and Bokeem Woodbine. Yune starred in the 2012 martial arts film, The Man with the Iron Fists, directed and written by RZA. His most recent role is Kang Yeonsak, the main villain, in the action thriller Olympus Has Fallen.