Glenn was born Theodore Scott Glenn in Pittsburgh, Pennsylvania, the son of Elizabeth, a housewife, and Theodore Glenn, a Business executive. He has Irish and Native American ancestry. During his childhood he was regularly ill, and for a year was bed-ridden. Through intense training programs he recovered from his illnesses, also overcoming a limp. After graduating from a Pittsburgh high school, Glenn entered The College of william and Mary where he majored in English. He joined the United States Marine Corps for three years, then worked roughly five months as a reporter for the Kenosha Evening News, located in Kenosha, Wisconsin. He tried to become an author, but found he could not write dialogue that satisfied the readers. To learn the art of dialogue, he began taking acting classes. Glenn made his Broadway debut in The Impossible Years in 1965. He joined George Morrison's acting class, helping direct student plays to pay for his studies and appearing onstage in La MaMa Experimental Theatre Club productions.

He married Carol Schwartz in 1968 and upon their marriage, Glenn converted to Judaism (his wife's faith). That same year, he joined The Actors Studio and began working in professional theatre and TV. An early television role was that of Calvin Brenner on the CBS daytime serial The Edge of Night. In 1970 Director James Bridges offered him his first movie role, in The Baby Maker, released the same year.

Glenn spent eight years in Los Angeles, California, acting in small roles in films and doing TV stints, including a TV movie Gargoyles. Glenn left Los Angeles with his family for Ketchum, Idaho, in 1978, and worked for the two years he lived there as a barman, huntsman, and mountain ranger, occasionally acting in Seattle stage productions. He then appeared in Francis Ford Coppola's Apocalypse Now (1979) and worked with Directors like Jonathan Demme and Robert Altman.

In 1980, he appeared as ex-convict Wes Hightower in Bridges' Urban Cowboy. After that he starred in the World War II horror film, The Keep (1983), and action films such as Wild Geese II (1985) opposite Laurence Olivier, Silverado (1985), The Challenge (1982) and drama films such as The Right Stuff (1983), TV film Countdown to Looking Glass (1984), The River (1984) and Off Limits (1988) as he alternately played good guys and bad guys during the 1980s. He returned to Broadway in Burn This in 1987. That same year he tried his hand at gangster movies when he starred as the real-life sheriff turned gunman Verne Miller in the movie Gangland: The Verne Miller Story which was given a theatrical release only in Finland and went straight to video in the U.S. In the beginning of the 1990s his career was at its peak as he appeared in several well-known and/or blockbuster films such as The Hunt for Red October (1990), The Silence of the Lambs (1991), Backdraft (1991) and The Player (1992). He played a vicious mob hitman in a critically acclaimed performance in Night of the Running Man (1995). Later he gravitated toward more challenging movie roles, such as in the Freudian farce Reckless (1995), tragicomedy Edie and Pen (1997) and Ken Loach's socio-political declaration Carla's Song. In the late '90s Glenn alternated between mainstream films (Courage Under Fire (1996), Absolute Power (1997), independent projects (Lesser Prophets (1997) and Larga distancia (1998), written by his daughter Dakota Glenn) and TV (Naked City: A Killer Christmas (1998). He was also cast in a supporting role in Training Day (2001). Glenn was cast in the FX drama Sons of Anarchy (2008) as Clay Morrow but he was replaced after an early pilot episode by Ron Perlman. He portrayed Eugene Van Wingerdt in a leading role, in the thriller film The Barber.