The Hollywood star was aged 86.
In a statement, his family said they shared the news of his death with "heavy hearts".
"To the world, he was a martial artist, actor, and a symbol of strength," the family posted on Instagram.
"To us, he was a devoted husband, a loving father and grandfather, an incredible brother, and the heart of our family."
Norris was hospitalised in Hawaii for an undisclosed condition earlier this week.
The martial arts expert turned actor starred in a slew of action films, since his acting debut with a cameo in a 1968 Dean Martin film, The Wrecking Crew.
Four years later, his epic fight with the kung-fu superstar Bruce Lee in The Way of The Dragon helped turn Norris into an icon on big and small screen alike.
