The 76-year-old, who played Hershel Greene in The Walking Dead, is said to have "lived at the emotional core" of the show.
Wilson played Georgia farm owner Hershel Greene in the post-apocalyptic zombie show from 2011 to 2014.
The veteran actor died on Saturday after suffering from leukaemia, according to celebrity news site People.
AMC said in a statement that Hershel lived at "the emotional core" of the show.
The TV network tweeted: "Scott will be remembered as a great actor and even better person."
Khary Payton, who plays King Ezekiel in The Walking Dead, posted: "The first time I met Scott Wilson, he gave me a big hug and said this thing I had become a part of.. was a family."
The show's executive producer, Gale Anne Hurd, wrote: "Scott was one of the greats, both as an actor and a man."
She added: "He is now a shining light in star in heaven spreading kindness and light forever."
Wilson was due to reappear in season nine of The Walking Dead and had already filmed his scenes for the forthcoming series.
Wilson appeared in his debut film In The Heat Of The Night in 1967, and played the murderer Robert Hickock in 1967's In Cold Blood.
He later appeared in Francis Ford Coppola's cinematic version of The Great Gatsby in 1974.
The actor leaves behind his wife Heavenly Wilson, who he married in 1977.
Chris Hardwick, who hosts Walking Dead aftershow Talking Dead, has paid tribute to Wilson in an Instagram post.
He wrote: "All of the best parts of Hershel Greene came from Scott - he was incredibly sweet, warm, and wise.
"When we lost Hershel on the show it was a week after my own father passed away and when Scott came on he Talking Dead he said so many kind and wonderful things to me afterwards that brought me great comfort."