Holbrook's assistant Joyce Cohen confirmed to the New York Times that he died Monday at his home in Beverly Hills, Calif.
Holbrook's ex-wife Carol Rossen also confirmed his death to the Los Angeles Times.
The actor began his one-man show Mark Twain Tonight! in 1954 and performed as Twain on The Ed Sullivan Show.
He opened Mark Twain Tonight off Broadway in 1959 and toured the United States, Canada and Europe before bringing the show to Broadway in 1966. He received an Emmy nomination after delivering a televised version of the show on CBS in 1967.
Holbrook continued to portray Twain onstage 20 or 30 times a year by 2009.
Holbrook also starred as Deep Throat in All the President's Men, Abraham Lincoln in a 1974 mini-series that earned him an Emmy, The Bold Ones: The Senator where he won an Emmy and Pueblo where he earned another Emmy.
He was a regular on television series Designing Women, portrayed Willy Loman in Death of a Salesman, was nominated for an Academy Award for starring as a lonely widower in Into the Wild and was Preston Blair in Steven Spielberg's Lincoln.
Other film roles include The Group, Magnum Force, Julia, Wall Street, The Firm and The Majestic.