He died at home in Los Angeles with his wife and family by his side, a statement posted on social media said.
Boseman was diagnosed with colon cancer four years ago but had not made the information public.
The news has left fans and the film world stunned. Get Out director Jordan Peele said it was “a crushing blow”.
“A true fighter, Chadwick persevered through it all, and brought you many of the films you have come to love so much,” his family said in the statement.
“From Marshall to Da 5 Bloods, August Wilson’s Ma Rainey’s Black Bottom and several more – all were filmed during and between countless surgeries and chemotherapy. It was the honor of his career to bring King T’Challa to life in Black Panther.”
Boseman came to prominence playing real-life figures – baseball great Jackie Robinson in 2013’s 42, and soul singer James Brown in 2014’s Get on Up.
However, it will be as the titular Black Panther in the blockbuster 2018 film he will be best remembered.
Boseman stars as the ruler of Wakanda, a fictional African nation with the most advanced technology on earth.
As well as winning critical praise and taking more than $1.3 billion US dollars (£973m) at cinemas worldwide, the film was widely seen as a cultural milestone for having a largely black cast and a black director, Ryan Coogler.
Boseman said last year that the film had changed what it means to be “young, gifted and black”.