"It is with heavy hearts that our family shares the sudden passing of our beloved Chuck Norris yesterday morning. While we would like to keep the circumstances private, please know that he was surrounded by his family and was at peace," the family said in a post on Instagram.
"To the world, he was a martial artist, actor and a symbol of strength. To us, he was a devoted husband, a loving father and grandfather, an incredible brother, and the heart of our family."
Norris made his film debut as an uncredited bodyguard in the 1968 movie The Wrecking Crew, which included a fight with Dean Martin.
He had also crossed paths with Bruce Lee in martial arts circles.
Their friendship - sometimes as sparring partners - led to an iconic face-off in the 1972 movie Return of the Dragon, in which Lee fights and kills Norris' character in Rome's Colosseum.
He went on to act in more than 20 movies such as Missing in Action and Sidekicks.
"I wanted to project a certain image on the screen of a hero. I had seen a lot of anti-hero movies in which the lead was neither good nor bad. There was no one to root for," Norris said in 1982.
In 1993, he took on his most famed role, as a crime-fighting lawman in TV's Walker, Texas Ranger.
The show ran for nine seasons, and in 2010, then-governor Rick Perry awarded him the title of honorary Texas Ranger.
The Texas Senate later named him an honorary Texan.
"It's not violence for violence's sake, with no moral structure," Norris told the Associated Press in 1996, speaking about the show.
"You try to portray the proper meaning of what it's about - fighting injustice with justice, good vs. bad … It's entertaining for the whole family."
Before he would become a star in movies and on TV, Norris was wildly successful in competitive martial arts.
He became a six-time undefeated World Professional Middleweight Karate champion.
He also founded his own Korean-based US hard style of karate known sometimes as Chun Kuk Do and the United Fighting Arts Federation, which has awarded more than 3300 Chuck Norris System black belts worldwide.
Black Belt magazine ultimately credited Norris in its hall of fame with holding a 10th degree black belt, the highest possible honour.
Norris made his last film appearance as himself in Australian action comedy film Zombie Plane, an upcoming movie starring Vanilla Ice.
"He lived his life with faith, purpose and an unwavering commitment to the people he loved. Through his work, discipline, and kindness, he inspired millions around the world and left a lasting impact on so many lives," his family said.
"We know many of you had heard about his recent hospitalisation, and we are truly grateful for the prayers and support you sent his way.
"As we grieve this loss, we kindly ask for privacy for our family during this time.
"Thank you for loving him with us."
"Chuck Norris Facts" went viral online after his comedic appearance in the 2004 movie Dodgeball, with such wildly hyperbolic statements as "Chuck Norris had a staring contest with the sun - and won," and "They wanted to put Chuck Norris on Mt Rushmore but the granite wasn't tough enough for his beard".
Norris ultimately embraced the absurdity of the meme craze, putting together The Official Chuck Norris Fact Book, which combined his favourites with supposedly true stories and the codes he aimed to live by.
He also write books on martial arts instruction, a memoir, political takes, Civil War-era historical fiction and more.
Norris celebrated his birthday just over a week before his death, posting a sparring video on Instagram.
"I don't age. I level up," he wrote.
with AP and Reuters
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