The star, who was nominated for an Oscar for his performance in The Right Stuff in 1983, died at his home in Kentucky on July 27.
A spokesman for the family said he died from complications of amyotrophic lateral sclerosis (ALS).
Born in 1943, Shepard grew up on a California ranch and went on to become an actor and prolific playwright, penning more than 40 plays.
Game Of Thrones star Nikolaj Coster-Waldau was among those to pay tribute.
He wrote on Twitter: “A hero of theatre. A hero of writing. A hero of acting. A hero of mine. Sam Shepard RIP.”
House Of Cards creator Beau Willimon wrote: “Sam Shepard is one of the greats. These eyes saw so much, and he wrote of what he saw with fearless, timeless honesty. RIP maestro.”
Novelist Chris Bohjalian tweeted: “”When you hit a wall - of your own imagined limitations - just kick it in.” - Sam Shepard. #RIP. You gave us so very much. You’ll be missed.”
Seinfeld’s Jason Alexander wrote: “A great man of the theater has passed. Thank you, Sam Shepard. RIP.”
The Shield star Michael Chiklis said: “First became a Sam Shepard fan as a playwright when I was in Buried Child @BU_SOT Tremendously talented actor as well. Gone too soon. RIP.”
Shepard wrote the Pulitzer Prize-winning Buried Child in 1979.
A production of the play, starring Ed Harris and Amy Madigan, finished a run at London’s Trafalgar Studios earlier this year.
The star’s films included Black Hawk Down, Fool For Love, The Notebook and August: Osage County and he recently appeared in Netflix series Bloodline.
Shepard was in a relationship with actress Jessica Lange for almost 30 years and they had two children together.
He had another child with his former wife O-Lan Jones.