Mr Zephaniah was also a Dub Poet who played the role of Jeremiah Jesus in Peaky Blinders.
A statement from Mr Zephaniah’s family posted on Instagram said: “It is with great sadness and regret that we announce the death of our beloved husband, son and brother in the early hours of this morning 7th December 2023.
“Benjamin was diagnosed with a brain tumour eight weeks ago.
“Benjamin’s wife was by his side throughout and was with him when he passed.
“We shared him with the world and we know many will be shocked and saddened by this news.
“Benjamin was a true pioneer and innovator, he gave the world so much. Through an amazing career including a huge body of poems, literature, music, television, and radio, Benjamin leaves us with a joyful and fantastic legacy.
“Thank you for the love you have shown Professor Benjamin Zephaniah."
Birmingham MP Shabana Mahmood wrote: "A son of Handsworth and the Windrush generation, Benjamin Zephaniah spoke in the voice of Birmingham’s migrant communities.
"He showed the country the best of our city and modern Britain.
"A true giant whose legacy will live on for generations to come."
Cillian Murphy said Mr Zephaniah was a “beautiful human being” in a tribute to the poet.
In a statement to the PA news agency, Murphy said: “Benjamin was a truly gifted and beautiful human being – a generational poet, writer, musician and activist.
“A proud Brummie and a Peaky Blinder. I’m so saddened by this news. RIP.”
Musician and activist Billy Bragg posted on X, formerly Twitter: “Very sorry to hear this news. Benjamin Zephaniah was our radical poet laureate. Rest in power, my friend.”
Mr Zephaniah was born and raised in Birmingham which he referred to as the "Jamaican capital of Europe.
His father was a Barbadian postman, and his mother was a Jamaican nurse.
He turned down an OBE in 2003 writing: "Benjamin Zephaniah OBE - no way Mr Blair, no way Mrs Queen. I am profoundly anti-empire."
In 2008 he was ranked one of Britain's top 50 post-war writers by The Times.
His autobiography The Life And Rhymes Of Benjamin Zephaniah was nominated for the Costa Book Award in 2018.
The X account for Premier League football club Aston Villa posted: “Everyone at Aston Villa is deeply saddened by news of the passing of legendary writer and poet, Benjamin Zephaniah.
“Named as one of Britain’s top 50 post-war writers in 2008, Benjamin was a lifelong Aston Villa fan and had served as an ambassador for the @AVFCFoundation.
“The thoughts and condolences of all at the club are with his family and friends at this time.”
Fellow writer Michael Rosen said he admired, respected and loved Mr Zephaniah.
He wrote: “The tragic terrible news has come to me that Benjamin Zephaniah’s family have announced that Benjamin has died.
“I’m devastated. I admired him, respected him, learnt from him, loved him. Love and condolences to the family and to all who loved him too.”