The actor died of natural causes at Cedars-Sinai Hospital in Los Angeles on Friday, reported Variety.
He had a high-profile role as manipulative cult leader Roman Grant on HBO polygamy drama "Big Love," which ran from 2006-11, and recently appeared as Carl Rodd in the "Twin Peaks" revival on Showtime.
His most recent film, "Lucky," about an atheist who comes to terms with his own mortality, is set to be released by Magnolia on September 29.
"Twin Peaks" creator David Lynch paid tribute to the star on social media, saying, "There went a great one. There's nobody like Harry Sean. Everyone loved him. And with good reason.
Director Edgar Wright tweeted, "RIP to the legendary Harry Dean Stanton. Impossible to cover his legacy in brief but here's a few favs: 'Alien', 'Paris Texas', 'Repo Man' (sic)."
"Pretty In Pink" actor Jon Cryer tweeted, "Was an honor, man (sic).