"We came to a collective decision that we are all the winners," Cammock said in a statement for the quartet.
"The issues we each deal with are inseparable," she said.
Cammock said the artists had not met before but agreed to act collectively at their first meeting after they were shortlisted, "in the name of commonality, multiplicity and solidarity in art and in society."
"The jury felt such a shared commitment should be recognized," said Edward Enninful, editor-in-chief of British Vogue magazine.
Enninful presented the prize at a televised ceremony at the Turner Contemporary gallery in the eastern seaside town of Margate, near London.
Cammock said the artists had united against issues including rising racism, social divisions and the "hostile environment" on immigration created by Prime Minister Boris Johnson's ruling Conservatives.
"This year, as it has often done in the past, the prize has sought to expand what it means to be British," she said.
"We find this significant in an era marked by the rise of the right and the renewal of fascism, in an era of the Conservatives’ hostile environment that has paradoxically made each of us and many of our friends and family again increasingly unwelcome in Britain."
Murillo told BBC that the Turner Prize "is alive and kicking.. precisely because of what's happened this year."
"We have very strong individual voices in what we do ... then we kind of realized, let's bring art into the [public] conversation," he said.
Film and multi-media artist Cammock explores social histories through "marginalized voices."
Her Turner-nominated solo exhibition "The Long Note" is a film about the role of women in the civil rights movement in the Northern Irish city of Derry/Londonderry in 1968, as a period of sectarian conflict was beginning.
Self-taught surrealist-feminist artist Shani uses performance, film, photography and sculptural installations to create "dark, fantastical worlds, brimming with utopian potential," according to the Turner Prize organizers.
She was shortlisted for works reflecting her four-year, ongoing feminist project "Dark Continent."
Jordanian-born Abu Hamdan is an artist and "audio investigator" who explores political and human rights issues.
He was shortlisted for three projects that "evolved out of earwitness interviews" with former detainees of Syria's Saydnaya prison, in collaboration with Amnesty International and Forensic Architecture.
British based Colombian multimedia artist Murillo focuses on labour and migration in a globalized world. He was shortlisted for three exhibitions, including one at the 10th Berlin Biennale.
In Berlin, Murillo baked clay and corn together to form the basis of sculptures that resembled rocks or bread and were piled up or placed with stuffed cloth torsos printed with labour slogans and international trade routes, the organizers said.
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