Hal's son, David, tells us ... his father passed away of old age at his Beverly Hills home on January 23. We're told he had a number of medical conditions and was having trouble swallowing, but he did not have COVID-19 ... it was simply his time.

Holbrook's career began in the '50s when he developed and starred in the one-man stage show, "Mark Twain Tonight!" which earned him critical acclaim. He would go on to win the Tony for Best Actor in 1966, get his first Emmy nom in 1967, and played the famous American novelist for more than 6 decades ... and in over 2,200 shows.

Playing historical figures on stage -- along with TV and movies -- was a staple for Hal. Throughout his career, he also performed as Abraham Lincoln -- which won him an Emmy in 1976 for the miniseries, "Lincoln" -- and John Adams in the 1984 miniseries, "George Washington."

Most famously though ... Hal gained international stardom for playing Deep Throat in the 1976 classic, "All the President's Men," in which he uttered the famous phrase, "Just follow the money."

Holbrook more recently played Republican congressman Francis Preston Blair in Steven Spielberg's "Lincoln" as well.

Along with all his historical roles, Hal also racked up 12 Emmy nominations and 5 wins. He was married to Dixie Carter until her death in 2010, and had a recurring role on her hit show, "Designing Women." He also directed a handful of episodes.

Hal also appeared in popular TV shows "Evening Shade," and "The West Wing" and starred on both "The Event" and "Sons of Anarchy" when he was in his 80s.

Then, in 2008 at age 82, he became the oldest person ever nominated for an Oscar for Best Supporting Actor at the time ... for his role in 2008's "Into the Wild."

Holbrook's other notable credits over the years include the miniseries "North and South," and films such as "Julia," "The Fog," "Wall Street," "The Firm," "Hercules" and "Men of Honor."

Hal was 95.