The 57-year-old was a stand-up performer in his own right – and was perhaps best known for his sketches in the Chappelle Show, which sent up Hollywood stars including Rick James and Prince.
Murphy also worked extensively with his younger brother Eddie, co-writing the films Norbit and Vampire In Brooklyn.
In a statement, his family said “their hearts are heavy with loss”.
They added: “Charlie filled our family with love and laughter and there won’t be a day that goes by that his presence will not be missed.
“Thank you for the outpouring of condolences and prayers.”
Fellow comedian Chris Rock tweeted: “We just lost one of the funniest most real brothers of all time.
Lin-Manuel Miranda, who created the hit Broadway musical Hamilton, described Murphy’s storytelling as “hilarious and unforgettable”.
And DL Hughley, who recently toured with Murphy, said: “After every gig, he rushed home to be with his kids. He died with gigs on the books.”
Murphy had recently been filming episodes of the crime drama Power, which are due to be aired later this year.
Starz TV, the channel which broadcasts the series, said in a statement: “His talent shines in every scene.”
The performer’s wife, Tisha Taylor Murphy, died from cervical cancer in December 2009. He is survived by three children.
© 2017, Vale of Glamorgan Broadcasting CIC T/A: Bro Radio & Sky News.