Born in Kansas City, Missouri, to Dr. Charles Cooper and homemaker Mary Ann Cooper. He grew up on his father's ranch and graduated from college with a degree in agriculture. He studied acting at the drama school at the University of Missouri. He worked for a short time as a set designer. In the early 1980s he moved to New York, where he initially worked in construction. Having decided to pursue acting, he played supporting roles in theatrical productions.

From the mid-1980s he appeared in television series. His breakthrough in his film career was the role of former Marine colonel Frank Fitts in the Oscar-winning film American Beauty. In 2003 Cooper won the Academy Award and the Golden Globe for his supporting role in the film Adaptation. Among the actor's recent notable roles are Sergeant Neil Craig in Remember Me, Stephen MacRay in The Town, Antonio in The Tempest, and Tex Richman in The Muppets.